Also, just wanted to reassure you that your lifestyle is not "high risk." If you use condoms for penetrative sex consistently, then you aren't putting yourself at risk for HIV. You may want to talk to a doctor about PrEP, though. It's a viable option, particularly for gay men who are not in a monogamous relationship, and who live in an area where HIV rates are relatively high.
Oil is dangerous and is not recommended because it can cause a condom to break. However, your condom did not visibly break, and that's what the oil would do that would cause an HIV risk for you. You can rest assured that if the condom was visibly intact, you didn't have a risk for HIV from that encounter. Although popular, mythical "microscopic holes" in condoms don't exist and wouldn't be a risk for HIV.
Oral sex is not considered a risk, so you can put that out of your mind.
HIV seroconversion rashes (aka ARS rashes) do not itch. Whatever is causing your rash is not related to HIV.
It sounds like that, in addition to the unknown, non-HIV rash, you have a common viral or bacterial illness. There is no event that you have described here that would be an HIV risk. There is no "something" that he could do to the condom that would be risky for HIV, that wouldn't also cause the condom to burst.