I’m truly sorry to hear about your pet. I’ve had rats as pets ever since I was 4 years old so I know how attached you can get to the little guys. I know female rats are very prone to breast cancer; a few of my female rats got it. I’m sure you have checked for lumps and I doubt breast cancer would cause the head tilt but it always caused an unbalance in the way my rats walked. I advise you to take her to another vet and take a stool sample of hers with you. I’ve experienced some veterinarians who will not give a rat the time of day so I just go to another one. Eventually I found a vet who would operate on my $3 PetSmart rats for $20 and even fashioned a little rat mouthpiece for anesthesia. Even if they can not help her a great deal, they can at least tell you the best course of action (be it rest and antibiotics or possibly euthanasia if there is not cure and to avoid pain). I’m sure that once being in the same cage as the bigger rat did not cause this. It is probably a health issue that was unavoidable. I’m also sure that she is doing a lot better than she could be because of how well you are caring for her. So, again, try taking her to a few more veterinarians and get the best answer you can. If the worst happens then just hold her and pet her and try and feel comforted that you’ve gave her a happy life.