1) what’s the possibility of me getting HIV if my cousin who has HIV used my toothbrush, had bleeding gums, didn’t wash the toothbrush good enough, and after that I used the toothbrush while having canker sores. I’m so scared that was a blood to open wound contact. 

1) In the nearly 50 years of the known world wide HIV/AIDS epidemic, there has never been a known case of HIV transmitted between housemates (who were not also sex- or needle-sharing partners) -- even though millions of them undoubtedly have shared toothbrushes. I'll also point out you ask a very unrealistic question:  What are the odds that all these things would come true?  Your cousin has HIV; AND used your toothbrush; AND he had bleeding gums; AND didn't wash the toothbrush afterward; AND you used it yourself when you had canker sores? IF all these things happened, I suppose there's a tiny chance you could catch HIV. But since it's a completely unrealistic scenario, I see no cause for worry.

2) How long HIV survives outside the body isn't the right question. However long it is, nobidy in the world has ever caught HIV from exposure to HIV infected blood or body fluids in the environment. But now you add another unlikely variable to the scenario just discussed above:  all the other things happened, AND you used the toothbrush so soon (wihtin a few minutes) that some blood on it had not yet dried.

These are zero risk scenarios and nothing for you to worry about. Trust me on this:  you will never get HIV until and unless you have unprotected sex or share drug injection equipment with an HIV infected person. Disregard all other possibiliteis and worries!

I hope these comments are helpful. Let me know if anything isn't clear.

HHH, MD

I’m in vacation right now and they also use reusable body wash at the hotel. I recently got a small surgery to remove a cyst and it got stitched up but it seems that the area still bleeds a little (on bandaid). I know I’m paranoid but it seems like transmission is quite possible. I would definitely seek help for my mental health.

"I know I'm paranoid" suggests you indeed are over worried about HIV, and perhaps germophobic in general -- and I support your intent to seek professional mental health care. Best wishes for it. In the meantime, you can be sure you will never acquire HIV unless and until you have unprotected sex or share drug injection equipment with an HIV infected partner.