Welcome and congrats on the BP! Sounds like you're making some wise investments to take care of her.
If your BP is a female and is 3 years old, then she is very underweight and has not been fed nearly enough if she's only been getting 3-4 mice a month. A normal adult BP can usually eat a medium rat every 7-10 days (and a medium rat is worth 3-4 mice on its own really).
I would start by buying a medium rat that's about the same width as the widest part of your snake and seeing if she will eat it. If she's been eating live, give her a live rat for now. If she'll take it, then you can try a frozen/thawed one next time.
Show us some pictures and I'm sure someone can help you determine her visible genetic traits. If you are not sure if it's a female, you can take it to a vet or breeder and they can help you determine the sex, or if you are confident working with reptiles you can look up popping and probing, the two methods for sexing BPs.
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