Hello, I'm Dr. Deb and will do my best to help you today.
Thank goodness you've rescued this little kitten; since she's so young, I hate to think what might have happened to her if you hadn't.
The fact that she's not otherwise acting ill is a very good sign. The most common cause of diarrhea and straining (which may be why her anal area looks abnormal and somewhat prolapsed) in a kitten this age is going to be internal parasites such as round worms. Other parasites such as coccidia, giardia, and hook worms are possible, too, but rounds worms are by far the most common.
The treatment I usually recommend would be pyrantal paomate which is available at many grain and feed stores. It is a very safe wormer and is very effective. I advise treatment every two weeks for three treatments. All cats in the household should be treated at the same time so they don't pass these worms back and forth if they share a litter box or groom each other.
It might also be helpful to start her on a good daily probiotic such as Forti Flora which may also be available at local grain/pet stores although it can also be purchased online as well.
As long as she's acting as a kitten this age should, then I might give her a few days to see if the stool issue resolves itself (with a few exceptions which I'll list below). It's even possible that the food she's now eating is not something she's used to and could be contributing to her looser stool issues; she may just need a few days to adjust to it.
However, if she becomes lethargic, stops eating, starts to vomit and/or her stools continue to be loose, then a vet visit would be prudent. I'm going to worry that she might have something more serious such as Panleukopenia which may require aggressive therapy.
Once she stops straining and after she's been wormed, the anal tissue usually returns to a more normal appearance. But, if the rectal tissue is significantly prolapsed, then she may need placement of what's known as a purse string suture to keep her tissue inside her body.
Since it's difficult for me to determine how severe her problem might be, a picture may be very helpful. This LINK walks you through the process.
I hope this helps and that her stools start to firm up soon. Deb