If you want to train you may need the sports science/kinesiology degree or your personal trainer cert.  I know that in Canada, you can train any individual or group EXCEPT a sports team with the personal trainer cert.  If you want to train a team you have to have a kinesiology degree as well.  Not sure if that would change if you had the physio degree or if the rules are the same elsewhere?

Easiest way to figure it out is to look up which schools have good physio and sports science programs and then send off a few emails or make some phone calls to those schools, explain what you want to do and they will be able to give you direction on what program is most relevant for you. 

You will likely make more money in the long run with a degree and it will open a few more doors for you career-wise, but it is also a much bigger monetary investment up front.   If you want a shorter investment period and a lower cost, a personal trainer might be a good choice.  You can do everything but fix within your scope as a trainer.  It really comes down to what you want to invest and what you want out of it.  

I recommend the reading, training, and shadowing awesome people as much as possible regardless of the education path you choose, but that won’t be enough to legally qualify you to train on it’s own.