Can HIV symptoms occur within a month of exposure?

Hello doctor,

I fear I may have contracted HIV. A month back, I had oral sex and regular sex from an unknown girl. Three days later, I started to feel very sick, headache, cold in warm weather, tired, diarrhea, sweating in bed (I thought this could be food poisoning). A week later I felt better but had breakouts on my whole back (thought maybe from sweating in bed and training in severe heat the past week). A week back, I felt fine most of the day but once 4 PM hit, my throat started to hurt, I had a severe headache, cold sweats, very tired, fever at 102 F. Felt better by the next night except for the throat which still hurts when swallowing. My neck feel kind of stiff as well. I wondered how much stress can play a factor in producing symptoms, because the first time I was extremely stressed for a couple hours about something and the second time the same thing. And I mean extremely stressed out and anxious, thinking alot, heart racing, etc. I of course will get a test but fear it is too early to show a positive result if it happens to be.