Marina,
First, it does sound like a classic cold sore. Second, she could have picked it up anywhere, especially if she's been ill with other things and her little system is a bit run down. Our gp maintained that kids just "pick them up." Ds was about 18 months when he got his first one--a little older than your dd, admittedly. And for us it was clear how & why he got it: a visitor with an active cold sore decided to kiss ds on the lips. (I saw it happen, and was unable to stop it in time. You can imagine how often I beat myself up over that one!)
Anyway, his situation was much less dramatic than either goosey's or jimjams's. The cold sore stayed for about 10 days, no gingivostomatitis, a little temperature at first. And that's it. Unfortunately he then started getting cold sores about every 3 months for about a year, and then it petered off to about once every 6 months, which is about where we are now. He doesn't get a temperature with it BUT it often portends an upcoming viral infection--i.e. just after it goes, he'll get ill with a little sore throat or cold, probably due to his being a bit run down anyway.
Acyclovir may shorten the infection (ask your doctor if she's old enough for it) but I haven't found that to be the case. I think it's best to use zovirax & the like at the first tingle of infection (which you can't know with a baby or toddler!). So I just let it run its course each time ds gets one as it doesn't seem to bother him much. If your dd continues to get them as she gets older, it will be important to remind her not to kiss anybody at nursery when she has a sore.
I don't know about your catching it--good question for the doctor. Sorry to hear this, Marina. I hope you get some good news & good info from the gp tomorrow. Good luck.
Ohand if you fancy digging up archived messages, there are a few which talk about alternative remedies for cold sorestea tree oil & the like (?)--but I think some of the mums decided in the end that they don't actually work. This is some years back, now, so my memory may be off.