HIV transmission and testing

About 3 weeks ago I had a brief unprotected sexual encounter (I am a
male). There was approximately 5 seconds of unprotected
contact/penetration. I do not know who the woman is so I will be
unable to see her again. I do not know if she has HIV but I am
concerned about possible transmission.

I am curious about the risks of having contracted HIV. I did not have
any STDs or open sores or anything on my penis. Although I was
concerned I may have caught something based on some pains I was having
so the doctor gave me some antiobiotics and things seem basically back
to normal. How much contact and what types of physical environment
(e.g. open sores) is required for HIV transmission?

What is the normal timeline after possible transmission before getting
an HIV
test?