Yes you can because HIV results don't show right away, it can take months before you start showing any symptoms and the virus doesn't show in general blood tests either. You need to take a special HIV test.
I had unprotected sex with a stranger. I had a blood test 4 days after that, but it was not an HIV test - it was a general blood and urine test and everything was ok on it. I don't have any symptoms just feel tired and pain in my legs sometimes. Could I have HIV?