Hi happytoes, welcome to the board!
It is good you took photos of your daughter's rash. If it changes, take more photos. If you are unable to post the photo here, you can email it to me at firstname.lastname@example.org Although only about 50% of people who have Lyme ever get a rash, a bull-eye rash is a definite sign of Lyme. There are other tyupes of Lyme rashes also. Here are a few sites where you can see Lyme rash photos:
Does your daughter's rash look like any of these? I don't think you are being paranoid at all, you are being cautious. I am sorry your sister is so sick. I hope she is getting treated by a knowledgeable doctor. If you need a doctor recommendation for her, feel free to email me.
If your daughter does have Lyme, the sooner she is properly treated the better. She is very lucky to have such a good mommy!