Pre-*** also carries sperm though it is in low quantities. Get a test and put your mind at ease. As for the sperm 10 mins before if you had cleaned yourself up low chance possibly not pregnant.
Well, sweetheart, unfortunately if you had come only five or ten minutes before, there is a chance (not the very highest of chances, but still a chance), because the pre-ejaculatory fluid coming through your urethra could or would have picked up sperm from the prior ejaculation. If you want more specific information on that possibility and how it works, google Cowper's gland.
If there was sperm put into her system by riding out of you on your pre-ejaculatory fluid, then the second part of the question of whether she could have gotten pregnant, is when she might have ovulated this past month. Six days before her period is due is a bit late for your girlfriend to have been ovulating, a fact highly in your favor. She would be much more likely to have ovulated 14 days before her next period is due. How regular are her periods, such that she can count on the date her period was due, to be pretty reliable?
Unlike your sperm, which (for your future information) can last quite a few days in her reproductive tract, her eggs only are viable for only a max of about a day and a half. Therefore, it might have been too late in her cycle for your little slip to have gotten her pregnant even if you did put sperm into her system.
If she has missed the length of a whole period (not just being late for the first day), it is a good time for her to take a pregnancy test. Even a Dollar Store test would be able to detect a pregnancy reliably by now. Be a good boyfriend and go there or to a drugstore and buy her a sensitive test (the ones from the Dollar Store are good, as are any marked "early results.") She should take the test with first-morning (concentrated) urine. She may find that her period is absent merely from her stressing over the issue.