congratulations! I've found therapy to be filled with all sorts of fears, but it has been really really helpful. I've found the most judgmental party in the whole enterprise has been me. It's totally normal to be scared, and have all sorts of fears. I found considering each of them and having a plan (ie if I'm too sick to go home after a session -what will I do, I can ask them to call a good friend of mine to come and get me, etc.) As it's turned out I've never had to to do that, but just knowing that if I need to I can do something about it has helped.
Also, for a long time I had 2-3 days after each session of not feeling too well. So I learned to try to plan my session, and think of my week accordingly. In my mind I compared it to chemo (not at all the same thing I know), but it's something that in treating it often makes you feel ill, but the goal is to make you better over the longer term. Be kind with yourself, understand that it's normal to find it hard, and remind yourself that it will get better, that every day won't be like the bad the days, and that feeling anything likely means you are getting somewhere.
It also took me awhile to stop seeing therapy and the therapist as a threat in some way, they are your ally and they want you to get better. Of course, you need to do a lot of work yourself, but they are there to guide you, to help you pace yourself, etc.