Is it possible for prior army infantry with no other schooling to switch to airforce TACP or would I need some kind of extra training?

TACP has their own selection with a pretty low pass rate and their own very long pipeline as well.

Here's a web site that describes TACP. https://www.airforce.com/careers/detail/tactical-air-control-party-specialist-tacp

-First, you would have to enter the Air Force as a prior service recruit. Not always easy.
-Air Force Recruiter can possibly get your headed for TACP specialist AFSC. You'll need to pass physical and score high on aptitude test.
-You will probably attend AF Basic Training, then you will have over a year of very challenging training to become a TACP specialist. It's equivalent to Army Ranger school in terms of physical and mental demands. It includes things like radio maintenance and lots of survival training.
-You'll need to learn to think in three-dimensional space so you can visualize and control different types of aircraft supporting the ground unit you're with. You will work with ground attack aircraft (A10, F35, F16, FA18) and some transport aircraft (OV22, C130, C17). You'll build an understanding for what we used to call the air-land battle.

It's a very challenging and well respected career field in the Air Force. TACP are in high demand and there are few of them, so you'll probably spend as much time deployed as Army Special Forces.

You will have to get a Green to Blue transfer approved and then go through half a dozen schools before becoming a qualified TACP.