I dont think you have an infected falopian tube or bowel . You'd have fever, malaise besides the pain and It would definitely show up in your white blood count and earlier than a month after surgery.
Although your symptoms started only one month ago and after surgery, it may not be related to surgery itself.
Have they considered irritable bowel syndrome? -maybe a diet high in fiber, drink lots of water would improve your symptoms. If this doenst work it could be adhesions - even more so if besides the falopian tube ligation you have had other surgeries before- ....
Anyway this is not a medical diagnosis but only an opinion cauze i havent seen your records or yourself personally so it is not apropiate to just give a diagnosis like that . hope it helps