Welcome to our Forum. As I am sure you know, I can provide some statistical information which will help to place your risk for getting HIV from your partner in context and which I hope will be helpful in relieving your concern. Here are some important facts:
1. Most importantly, you have had the HPV vaccine. In the studies used to evaluate the protective effect of the vaccine on risk for warts, the vaccine provided 99% protection.
2. Further, with respect to your concern about the other HPV types, types 6 and 11 are two of the types found in the vaccine your received and these two HPV types cause well over 90% of visible genital warts.
3. You note that your partner was treated in July. Typically if warts are going to return, they do so in 3-6 months. the more time that has passed since his treatment without a recurrence, the lower the likelihood that he has infectious virus present and remember, even if he does have a recurrence, the vaccine is likely to be protective for you).
4. FYI the timeline your partner has provided is consistent with his getting infected by his other partner in February.
Bottom line, your risk for getting warts from your BF is very low, mostly because you have received the HPV vaccine. If you want to be extra carefully condom use for a few months for genital sex will provide extra, added protection.
I hope these comments will be helpful. Your risk for warts is small and even if you should get one, they really are more of a nuisance than a health hazard. Take care. EWH