welcome to YT!
When a dog rubs it's bum it usually means their anal glands need to be expressed. Some dogs do this on their own and some need help from a vet or groomer (i don't do it myself). Has he been to the vet since you had him?
Did he only throw up once? Was it food?
I think most Yorkies are escape artists!
I bought this for my dogs:
Amazon.com: Pink Pet Tent Exercise Pen Playpen...
It's collapsible and portable. It a top also so that your pup can't escape.
What's his name? Photos?