I got a positive urine pregnancy test 3 days after intercourse, is it possible that soon to tell?

Much to soon for any test to be accurate.
That is why they are meant to be used AFTER your first missed period AFTER intercourse.

I missed my period 3 days later

So your basically 3 days late then ?

If you are that concerned then an examination with your own medical practitioner would be in order.

I had sex on the 13th of may. Took a pregnancy test on the 16th and it was positive. Was due to come on the 19th and didn't. I am 8 weeks pregnant just asking was it possible from that encounter or from one I had May 6.

Well that changes things and also highlights the importance of giving the complete picture.
If you have a concern surround paternity then you will have to schedule a DNA test with all of the affected parties.
It's best AFTER the birth for maximum safety of the child.