Does Shelly have mites?

Since she is scratching a lot and her sister had hair loss, I'd recommend treating her.
This page will tell you which medication to use.
https://www.guinealynx.info/mites.html

Since she's from a breeder, I'd also recommend taking her to a vet to get a health check.

My advice is, definitely treat for mites. I have read that mites can lay dormant for a while and sprout up unexpectedly. Hair loss is a sign of more than just mites though, such as scurvy and ovarian cysts, and scratching is also a sign of more than just mites. So Shelly should get a full check-up from a cavy savvy vet!
Wait you said you got her three weeks ago, and she hasn't been drinking any water since you got her...so she hasn't had any water in three weeks?! hmy: That is troubling! Did she have a bottle before? Is it too high up? Maybe offer a dish of water as well as the bottle and see if she drinks from that. And of course the vet.

I'll take her to a vet, but isn't it really expensive? Can't I just use ivermectin?

Vet fees vary by locations. You can treat mites with Ivermectin, but you might want to have a vet check on her in case she has other problems.

I always had the perception that vets cost lots of money, but actually, for a regular exam on a cavy, it's way less than I originally thought it would be! Of course it varies vet to vet, but I dare to say roughly $50, give or take $15? Medication would be extra, though. Maybe others can help me out here :?:

I'll hopefully be going to the vet tomorrow and we pay about $50.00 before any medications. I too believe my little man might have mites. This is so discouraging because he was just treated for a possible abscess. We don't have any itching but I just noticed a shorter hair patch (he's a texel) some flaky spots, and a little sore on his little black skin

Where do mites come from? Guinea pigs don't really go outside, no-one else is in their cage, so how do they get them?

Petlovr, some experts think guinea pigs always have them, and that they just have outbreaks now and then. But mites are pretty much everywhere, on your bed, your furniture, you... Not a happy thought!

I'm rather new to the whole Guinea Pig thing, so forgive me if some questions seem basic. Do the mites outbreak or overwhelm the piggie because of an underlying health problem, or because they are stressed (this happens with fish and ich outbreaks), or do the mites become a problem for no reason at all? Do they have to go to the vet, or is there over-the-counter medicine at the pet store?