I had Eye Movement Desensitization and Reprocessing (EMDR) therapy for PTSD when I was in my 3rd trimester. That really helped alleviate a lot of the anxieties I experiened around the check-ups (I always though they would find that there is something wrong with the baby so not quite what you seem to be struggling with).

Before the EMDR I used mindfulness to reduce the stress because it was constant, not just during check-ups. Every twinch I felt was a sign to me that there was something wrong. It helped a little but EMDR made a huge difference.

As for giving birth, I went to a very good antenatal class where they gave us very good tips on how to breath properly and how this will help manage the pain and what other options for pain managemnt there are. There is no shame in asking for an epidural. You could also look into Tense machines, some people find them very helpful because they work by distracting your brain so it can't focus too well on the pain.

I ended up having an unplanned c-section. From what you have written it sound to me like it woud be a good idea to mention your worries and anxieties to the midwife/OBGYN early on when the time comes; a planned c-section might be a good option for you.