In the first place, your girlfriend has it backward. A woman doesn't usually ovulate 10 days AFTER she begins a period; she has already ovulated about 10 days BEFORE she begins a period. If she begins menstruating, that means ovulation has already taken place and she didn't get pregnant. Her cycle begins on the first day of her period, every month. If she's on a 28-day cycle, she will usually ovulate on the 14th day after Day One of her period. The number of days her menstrual flow lasts is immaterial.
WHEN are young people going to stop worrying about "pre-ejaculate" (or "precum")? It's nothing more than the natural lubrication fluid that a male always secretes from the tip of his penis when he is sexually aroused. 97% of the time, it does NOT contain sperm cells. You could rub it all over her vulva, and it's highly unlikely that she would get pregnant.
Why don't you go to some reputable internet medical sites (there are a number of them out there) and learn what "precum" is, and what it can and what it cannot do? Maybe then you won't worry about it so much.
What you SHOULD be worried about is ejaculation fluid (semen). Semen ALWAYS contains millions of sperm cells, and it takes only ONE sperm cell to cause pregnancy.. THAT is what makes a woman pregnant. If you ejaculate semen inside her vagina or rub it against her vulva, there's a high chance she can get pregnant.