Yes, OCD will make you doubt everything. It feeds on whatever your worse case scenario is at a given time. Right now, for you, it's 'all hope is gone'. That likely scares you to no end. I know because I get those thoughts too.
For me, things have started to improve by simply changing my perspective a little. Simply realizing that these unwanted thoughts/feelings/urges are not really the problem. The problem is how I have reacted to them in the past. The more I argue with, disprove or neutralize a given thought, the more likely I am to experience that thought again. That's just what the mind does. Your mind is really a sophisticated bio-machine, it's not you. Who you are consists of much more than your thoughts.
I really think you would benefit from seeing someone that specializes in CBT and possibly ACT (acceptance and commitment therapy).