hun what kind of cage are you keeping them in? I don't think it's working and I'd like to help you figure out how to prevent it. I have had experience with one escape artist but she was only ever able to escape out of the free play area by chewing out of it.
It sounds like there's a mixture of illness and insecurity going on. You haven't had them very long, and it takes a while for rats to establish trust. Have you examined her limbs to see if any of them are disabled or bothering her in any way?
I would consult with a vet immediately. I'm not sure what you mean by not having access to a vet at the moment, but if it is cost associated, look into the care credit card or borrowing a loan from a friend. When rats get sick they get sick FAST, but they recover fast if given proper care in a timely manner. I always get my rats to a vet within 48 hours of sickness/injury. Please try to get her to one. And I hope you find your other rat =(
I recommend you find a vet ASAP =( and definitely re evaluation your cage situation, if you will share a photo i'm sure we could help you find a way to prevent that from happening again. But i'm afraid the vet is a must! Rats get sick very fast and it's hard to get them to come back if you wait more than 48 hours to see a vet. Best of luck to you, hun
Are you sure her heart rate is too fast? Rat's heart rates are normally pretty fast, and the baby ones are slightly faster. Could something have spooked her? They will often act like you described, and it can be for something seemingly so minor. Especially for babies. Do they have plenty of places in their cage to hide, and play? Where is their cage located? It's best to have it in a busy part of the house, so they get used to all the sights, sounds, and smells faster. Also, it's not a bad idea to take them to a vet and get a health check, so you have a baseline to compare to for when they do get sick. Also, I would get kitten revolution, and keep it on hand, or go ahead and treat for mites. Most vets don't know what to look for in rats when it comes to mites, and they won't show up on a skin scrape test. Lilspaz can help you with dosing.