Can HIV be transmitted through oral sex?

Hi doctor,

27 days ago I had protected sex with a girl, whom I knew only for 5 days and it was the first time. Also, we had oral sex also. During oral sex, I had no protection. Next day I started having pain on my testicles and my stomach. I was feeling weak the whole time, and after a week I gave urine and semen for culture. The urine culture was clean, and the semen culture with bacterium E. coli has been detected. It is worth mentioning that I am suffering from prostatitis and I have been diagnosed and treated for more than 3 years with almost the same bacterium, which I thought has been eliminated. Also on that day, we had sex 3 times within 5 hours and I am thinking whether the intensity of that might have brought back the E. coli or it was still there and it appears now. I do not know therefore this is my first question. Since the oral sex was not protected, can it be that she passed me the E. coli? Or is it due to my prostatitis? After my semen results, the doctor asked me to take Tavanic 500 mg once per day for one month. I am now on the first week, the pain is still there but comparatively less. I still feel pressure on the lower part of my stomach and also since the last 3 weeks I feel my stomach always full and not so comfortable. Can this be a side effect of the E. coli or something else? I had no fever since then, and I did not lose my appetite, but I am feeling full. Apart from the E. coli that I need to finish my treatment, now I do have a fear whether I have been infected with any other STDs(Sexually Transmitted Disease). If yes, the semen and urine culture should have normally shown something abnormal. Also, I have a fear if because of the oral sex, I might have been infected with HIV (Human immunodeficiency virus), could this be possible? Should I do an HIV test? If yes which kind of HIV test can give me a fast indication. Thank you.