No, that does not sound like HIV.
It sounds like you are just breaking out from sweating and being on a dirty carpet. Even if the carpet does not look dirty, and even if it is freshly vacuumed, if you were sleeping directly on the carpet with no blankets or anything, that's kind of the equivalent of never changing the sheets on your bed. You wouldn't just vacuum your bed off, never change your sheets, and call it clean enough to sleep on, right?
So make sure you sleep on a blanket or sheet rather than directly on the floor or mattress. Wash your blankets and sheets. Never use a pillow without a pillowcase on it. Wash your pillowcases often. Make sure you are washing your back and shoulders when you shower.
So it sounds like your acne is just pain old acne. However, that does not mean you do not have an STD. Most people with STDs don't even have any symptoms. So if you're wondering if you're clean or not, all you can do is get tested.