I am about 19 weeks pregnant, i was wondering if its possible i became pregnant on may 17th using a condom and probably not ovulating. i also took a home pregnancy test 2 weeks after may 17th, would the test work 2 weeks after having sex?

Probably, yes: You don't give your last period, but if you are at all regular then may 17 is nearly exactly when conception should've occured. Yes, a home test is reliable at less than 2 weeks after conception. You don't say why you believe you are not ovulating, but apparently you did on or around may 17.

Agree with Dr. H: Under the right circumstances, home pregnancy test would be positive at 2 weeks after fruitful sex.