is a red rash on penis and redish around the tip a symptom of HIV??

hello on the 31st of october i finger a girl at a party i didnt know her and  was really drunk i have spoken to her since she says she has nothing and hasnt had unprotected sex of course you cannot rely on word alone..... ok so at the part i fingered her for a short while not too long but i did penertrate fairly deep.. after this had been done i found a cut/ opening on the area of my finger underneath the nail its also call ( rag nail) or something where i bite my nails at the btoom end of the nail as if u were getting closer to my knuckles but obviously up by my nail there was a cut and it was bleeding i dont know when this had happend as i didnt feel it...obviously i would like to know what is the risk if any i would also like to say that i have found a reddish rash on the tip of my penis and base of penis is this a symptom of hiv??

i am obviously quite worried and would apreciate any information

[Teak]

HIV is transmitted by:
Unprotected anal and vaginal sex
Sharing works with other IV drug abusers
Mother to child

At no time did you have a risk of contracting HIV from fingering.