How can I transfer from the USN IRR to the USAF (Reserve or Active Duty) to become a Combat Rescue Officer?

LTJG John A. Assuming that you can just cross-over, and not have to take AFOQT or OTS (because that would be redundant, right?). There is the indoc course at Lackland, along w/ many other courses. There's a reason they call it Superman School: (pasted from Wikipedia)

Pararescue/Combat Rescue Officer Indoctrination Course, Lackland Air Force Base, Texas (9 weeks)
The mission of the Indoctrination Course is to recruit, select and train future PJs and CROs. At this school, participants undergo extensive physical conditioning with swimming, running, weight training and calisthenics. This course helps prepare students for the rigors of training and the demands of these lifestyles. Other training includes obstacle courses, rucksack marches, diving physics, dive tables, metric manipulations, medical terminology, dive terminology, cardiopulmonary resuscitation, weapons qualifications, history of PJs, and leadership reaction course. Graduation of this course gives candidates a "ticket to ride the pipeline," where Pararescuemen begin learning the special skills that make PJs highly regarded special operators. Pararescue "Indoctrination course" has been replaced with a tougher Assessment and Selection (A&S) course. This course is similar in methods of workouts to its predecessor, however, at the end of the course, the instructors choose who will and will not go on to continue the Pararescue pipeline.

Pararecue Indoctrination Course Training Gear
— Indoctrination Course (currently A&S) Training Gear is essentially made up of a High Volume Face Mask, A Silicone Snorkel, Rocket Fins and Booties. The mask and snorkel are key throughout training, being used in water confidence training such as water inserted into the mask throughout the training, simulating the effect of being underwater regardless of whether submerged or not. Mask and snorkel recovery is a key portion that is tested on, in which the trainee has to recover the mask and snorkel from the deep end of the pool, "clearing" the mask of water while still submerged and "clearing" the snorkel of water as well. These two can be referred to as key training tools. Items such as rope and booties can be used to further increase the intensity of water confidence training.

Army Airborne School, Fort Benning, Georgia (3 weeks)
Students learn the basic parachuting skills required to infiltrate an objective area by static line airdrop. This course includes ground operations week, tower week, and "jump week" when participants make five parachute jumps. Personnel who complete this training are awarded the basic parachutist rating and are allowed to wear the Parachutist Badge.

Air Force Combat Diver Course, Navy Diving and Salvage Training Center, Naval Support Activity Panama City, Florida (5.5 weeks)
U.S. Air Force Pararescuemen from the 82nd Expeditionary Rescue Squadron, Davis-Monthan Air Force Base, AZ, walk their Zodiac to the beach after jumping out of an MH-53 Pave Low helicopter.
Pararescuemen and a simulated "survivor" watch as an HH-60G Pave Hawk helicopter comes in for a landing.
The course is divided into four blocks of instruction: (1) Diving Theory, (2) Infiltration/Exfiltration Methods, (3) Open Circuit Diving Operations, and (4) Closed Circuit Diving Operations. The primary focus of AFCDC is to develop Pararescuemen/Combat Rescue Officers and Combat Controller/Special Tactics Officers into competent, capable and safe combat divers/swimmers. The course provides commanders with divers/swimmers capable of undertaking personnel recovery and special operations waterborne missions. AFCDC provides diver training through classroom instruction, extensive physical training, surface and sub-surface water confidence pool exercises, pool familiarization dives, day/night tactical open water surface/sub-surface infiltration swims, open/closed circuit diving procedures and underwater search and recovery procedures. The session culminates with a waterborne field training exercise.

Navy Underwater Egress Training, Naval Air Station Pensacola, Florida (1 day)
This course teaches how to safely escape from an aircraft that has landed in the water. Instruction includes principles, procedures and techniques necessary to escape a sinking aircraft.
Air Force Basic Survival School, Fairchild Air Force Base, Washington (2.5 weeks)
This course teaches basic survival techniques for remote areas using minimal equipment. This includes instruction of principles, procedures, equipment and techniques that help individuals to survive, regardless of climatic conditions or unfriendly environments, and return home.

Army Military Free Fall Parachutist School, Fort Bragg, North Carolina, and Yuma Proving Ground, Arizona (5 weeks)
Air Force Pararescuemen jump from an HC-130P/N in support of Operation Enduring Freedom.
This course instructs free fall parachuting (HALO) using a high performance parafoil. The course provides wind tunnel training, in-air instruction focusing on student stability, aerial maneuvers, air sense and parachute opening procedures. Each student undertakes a minimum of 30 free fall jumps including two day and two night jumps with supplemental oxygen, rucksack and load-bearing equipment.

Pararescue EMT-Paramedic Training, Kirtland Air Force Base, New Mexico (37 weeks)
This course teaches how to manage trauma patients prior to evacuation and provide emergency medical treatment. Phase I is seven[10] weeks of emergency medical technician basic (EMT-B) training. Phase II lasts 30 weeks and provides instruction in minor field surgery, pharmacology, combat trauma management, advanced airway management and military evacuation procedures. Graduates of the course are awarded National Registry of Emergency Medical Technicians-Paramedic (NREMT-P) certification.

Pararescue Recovery Specialist Course, Kirtland Air Force Base, New Mexico (24 weeks)
Qualifies airmen as pararescue recovery specialists for assignment to any Pararescue unit worldwide. Training includes field medical care and tactics, mountaineering, combat tactics, advanced parachuting and helicopter insertion/extraction qualifications. At the completion of this course, each graduate is awarded the maroon beret.

Pararescue and Advanced Pararescue Orientation Course
Since the 1950s, Air Force Pararescueman have provided training and mentorship for Civil Air Patrol cadets. This was formalized in 1977 with the introduction of Pararescue Orientation Course (PJOC) at Kirtland AFB, New Mexico. PJOC was later taught at Fort Knox, Kentucky and George Washington National Forest, Virginia. The course teaches CAP cadets fundamental survival and rescue skills such as shelter building, land navigation, and rock climbing. Advanced Pararescue Orientation Course (APJOC) began in the 1980s and was taught only at Kirtland AFB. In 2003, both programs were cancelled. PJOC returned in 2004, but APJOC did not see its return until 2008 when the course was moved to Davis-Monthan AFB, Arizona. APJOC builds upon the skills learned at PJOC and exposes cadets to life in an operational Pararescue or Special Tactics Squadron. The course culminates with a Combat Rescue Training Exercise. During APJOC, Both PJOC and APJOC are Civil Air Patrol National Cadet Special Activities provided by United States Air Force Pararescue.

Sir, why not become a SERE swimmer, and stay Navy.

I would try to get in contact with a officer accessions recruiter for your region. There is different one for active duty versus reserves.

Thing to understand with officer recruiters is that they aren't really recruiters in the same manner as an enlisted. You will have to stay on top of them.