My girlfriend and I had unprotected sex two times in a row with a 15-20 minute brake (I withdrowed and ejaculated outside both times) on the 13th day of her cycle. Calculations suggest it might be the day after ovulation. Should we worry that pregnan?

Some sperm. can be released, even though you withdrew, though this does reduce the risk somewhat. A 20 % chance of pregnancy with ovulation and full ejaculation. Decreased chances, are to quantify, but certainly reduced, but not zero chance.
Sure, it can happen. A urine pregnancy test, done correctly, gives a reliable result 3 weeks after sex (3 weeks after when conception might have occurred), or 1 week after missing a period. If done sooner, a positive result is likely real, but a negative result may be due to testing too soon, and thus lead to a repeat test. If a woman gets her normal regular period, then she is not pregnant, and a test is not needed.