I think it is a coincidence, though. Your wife's rash sounds very non-specific, meaning that it could be a mild virus in the system or something like that. Eczema sounds much more likely than a yeast infection, by the way. I suggest that she see a skin doctor as soon as possible, so you'll both know what it is, and she can get treatment if she needs it. As to your guilt and anxiety, I'll leave that to you to work out. But I do not think you have given your wife (or yourself) AIDS.
If your wife has hiv, she didn't get it from your protected sex incident. That said, relax. It could be many things & it probably has nothing to do with hiv. HIV is a very hard virus to contract. For one time exposures it's like 1/2000. Stay safe.
Very unlikely that this is HIV. The symptoms are much more than just a rash. I believe that Dr. Rockoff has mentioned that they are flu like as well. If this is the only symptom, then it is probably just your every day rash that pops up all the time and means nothing. If you want to know for sure, go to the doctor and get tested for HIV. I am very sure it will come back negative, and then you can quit worrying about your wife. And be faithful in the future. It is one thing to cheat but you will feel terrible if at some point in the future you endanger your wife. I doubt that you have anything to worry about this time, but playing russian roulette with your life is one thing. Playing it with someone else's is unforgiviable.