What additional skill identifiers are available to 68W's?

This is what I found via Google. I would recommend you speak with your Training NCO to confirm

F2 is an Army Critical Care Flight Paramedic (Awarded after completion of the Flight Paramedic Course 300-F1/F2)
F3 is an Army Flight Medic
M6 is the Army's Licensed Practical Nurse
P1 is an orthopedics specialist (clinical)
Y8 is an immunization-allergy specialist (clinical, lab)
N3 is the Army's Occupational Therapy Assistant (clinical)
N9 is a physical therapy technician (clinical)
Y2 is the code used to identify those who have not finished the upgrade classes
W1 is a special operations combat medic (SOCM)
W2 is a Regular Army Civil Affairs medical specialist
W4 is an Army Special Operations Forces Civil Affairs medical sergeant
P3 is an optometry specialist (clinical)
Y6 is a cardiovascular specialist (Cardiac Catheterization Technologist and Echocardiographer)
P2 is an Ear Nose and Throat specialist (ENT)

The best thing about the medical field is there are many places to gain knowledge. Civilian certifications on your own time is great! Just ensure it benefits not only the patient but you in your civilian employment. But like the answer below. There are many schools available to lower enlisted. It just takes filling out the proper paperwork, supportive chain of command and you can do it.

Many of the 68W ASIs act more like SQIs, in the fact that they are used for assignment, rather than an "extra skill". W4, W1, F3 are the ones that will really change the career, but are probably the hardest to get without packets and tryouts

FWIW, a half million years ago, when medic was 91B, and 91C was LPN, there was a program in the USAR that permitted aspiring nurses to receive ADSW and a full scholarship to obtain their LPN. I can't tell you whether or not this still exists in some version or another, but I knew more than a few 91B who applied to the local junior college, dropped a packet at the unit, and were awarded 91C (now M6) after the successful completion of the school. A few then went ahead and completed their ASN and as a Registered Nuisance, we're eligible for commissioning with the caveat that they'd need to complete a Bachelor's degree before becoming eligible for field grade rank.

I'm a 91B and 91D and was discharged in 1984. That was a combat medic and a surgical technician, I went to RN school after I got out and I was so disappointed with how little respect nurses got compared to the commissioned officers in the Army, the pay wasn't much then for nurses and in civilian life they were almost the handmaids of physicians. I dropped out with only a semester to go. I bounced around selling this and that became a stockbroker for a year, finished a BS in Chemistry and worked at that for a few years and hated it. Oil refinery and a drug company. I applied to law school in 1990 and have been practicing law for almost 30 years. My youngest son was a 68W and he is on his way to being a physician.

Unrelated to 68W, but the army offers lean six sigma training to be a greenbelt for free. Regardless of duty status. It is also an ASI once you get the cert.