Can I get HIV from frottage with a males anus? (Possible anal fluids outside of anus)

No. Not unless you had a nasty bleeding sore where your rubbed. This is basically safe stuff. However... you also say you have "oral thrush." This may be from your being on doxycycline for a while, but if a competent physician diagnosed oral thrush, it's time to figure out why. Be brave and get yourself an HIV test to rule that concern out.