She is adorable, love her ears!! I hope you'll post more pictures of her after her groom!!
I actually do see what the groomer was talking about as I've had pups with hair like this in the past (identical to your picture). Just looking at her picture, I can tell you she is at least knotted in her chest and back. Once their hair starts changing, they often start tangling close to the skin, all over. Unless you are an experienced dog owner used to dealing with long haired breeds, you aren't going to see it. The brush you used skipped right over it. Use a comb from root to tip and you will see what she was talking about. She told you not to bath her because bathing a dog with already tangled/matted hair will make it worse, it sets them in more so please take her advice and don't bath her until all those tangles are out because you will only make it worse.
I can also understand why she said to shave her. Getting these out will be time consuming, not exactly the best for the groomer or puppy especially if the puppy hates being brushed. Shaving is the least time consuming and least uncomfortable solution for the puppy. If I were a groomer and a similar situation arose I would have said the same thing because grooming those knots out can be hard for a puppy to handle but I also would have took the time to show and explain to you what I meant because not everyone automatically knows these things and the groomer just came across as rude by not explaining herself.
Your not a bad mom at all, you just didn't know, many of us don't, it's a learning process. I admit, prior to getting a yorkie, I would have been the same way. Usually a simple brush will not work for a yorkie puppy as they don't reach the hair close to the skin. This is why a good brush and comb is important. If you can run a comb all along her hair from root to tip, your good to go as it will catch any tangles, snags or knots that the brush missed and you would be surprised how much the brush does miss.
I too love the madan brushes and combs Jenny sells and highly recommend them!!
I would also try the Espree detangling spray she has, I think it will do the trick for you getting rid of those knots as least painfully as possible.