Well, first, Welcome to Yorkie Talk
Great place for information and support.
I am not a nutritionist or a vet - have raised Yorkies for 17 years. My first question is has he stopped throwing since you went back to his previous food? If so then you need to staunchest for awhile till his stomach settles back down.
Next, yes you should get excited when they start the throwing up thing. He is very young and can dehydrate VERY QUICKLY and aspirate when he is vomiting.
You hit the nail on the head when you said you did not gradually introduce the new diet! So after things settle down you can start that VERY SLOWLY.
If you do home cooking you will need to use an additive like BALANCE IT in order for your pup to get all of the proper nutriments like vitamins and minerals. I order it on line.
I am sure others will come forth and add other important things for you to consider, such as, health insurance or Care Credit for financial help if you need it.
The good news here is that you were a front-and-center good Yorkie momma and looked for help when your baby had a problem. Stick with YorkieTalk - I can't tell you how much I have learned from these very smart, experienced and caring folks!