It doesn't sound like your problem is Interstitial Cystitis, which is an inflammation in the lining of the bladder. However, it's possible that it is; you may have multiple issues, as many do.
It does sound like there's an issue with the mesh that was inserted, first and foremost.
I'd recommend that you talk to your doctor. The transobturaror tape is supposed to be pretty fast healing, so at 3 months, you shouldn't be having a lot of trouble. I can't imagine what could poking your husband when you have sex. There shouldn't be anything. That really needs to be checked.
You may, also, have a vaginal infection that can cause the feeling that you constantly need to urinate, but you shouldn't have to be self cathing.
If the doctor who inserted the tape can't/won't help you, I'd strongly recommend that you find another doctor... preferably a uro/gyn who can test/treat, both, urinary and gynecological issues.