Congratulations on starting with a PT! And if you are new to exercise, you will definitely feel it for up to 48 hours afterwards. I still have sessions with my PT now where I struggle to sit down or climb stairs the next day if she's been extra harsh on me, and I've been seeing her for over a year! But it's a good sign that you are working your muscles, and it does get better with time.
My PT insists that I've had my morning shake before she trains me - your body needs some fuel in it, otherwise there is the risk of going lightheaded and injuring yourself - especially if you are using weights.