It was very painful and I had to take some rest, but I felt good afterwards because I felt I had done my part.

The way you wrote it was fine. I have provided 2 additional natural versions for your consideration:

I felt good afterwards because I felt like I had done my part.

I felt good afterwards because I felt as though I had done my part.

I’ll possibly have a surgery in the future, so it’s mutual.. So, I may end up benefitting from someone else‘s similar actions.

It was very painful and I had to take somesubsequently had to rest, but in the end I felt good afterwards because I felt I had done my part.

- In English we never say take some rest, we say take a rest. When you say take a rest though, it's typically used (at least in my experience) after having done some physical exertion. If you don't use any preposition and just say I need to rest, this could be for anything so I think it fits best here.
- Changed afterwards to 'in the end' to be explicit that you felt this after you had rested which was explicitly after the painful part where you had your blood drawn

I’llt's possibly have ae that I'll have surgery in the future, so it’s mutual.

- Reworded the first bit to sound more natural. It's grammatically correct but it's not usually said in that manner
- In English we don't 'have a surgery' we just 'have surgery'
- It's mutual doesn't make sense here but I'm not sure what you were trying to say. It's mutual means a feeling you have about something is shared by another person. E.g I love him and it's mutual means I love him and he loves me back (because it's mutual i.e you both share the same feelings). Surgery can't have feelings back for you so you can't use that phrase here. Please comment what you were trying to say and I'll come up with a correction for you