Good Morning and welcome! I am Dr. Loretta, a licensed veterinarian and I am happy to answer your question.
Oh my! Poor little Terry! It sounds more like this encounter has stressed Terry out so much that it is causing a digestive disturbance. Yorkies are very sensitive and when they are stressed, this can happen. It is probably minor and is treated as follows:
Fast Terry for 12-24 hrs to allow the digestive tract to calm down and heal.
Give him Pepcid AC or Famotidine
at 0.5 mg per pound every 8 hrs. That can be purchased over the counter at the pharmacy.
Give only small amounts of water during the fast or ice cubes
After the fast, feed rice and boiled chicken
If the vomiting has resolved, then wean Terry back onto regular food. If the vomiting persists especially during the fast, take him to your vet for an exam and lab work to determine the cause for this. This is extremely important since this can cause dehydration or other more serious concerns.
Rats do not carry rabies in general but this can be a concern...if Terry does not respond, take him to your vet.
Does that make sense to you?
Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please REPLY so I can clarify for you.
Sincerely, ***** *****