Hi! I'm going through the same issue, it's definitely worrying so I completely understand. Our pups are about the same age and weight but about a month(?) ago when I took her in for vaccines she had a bad reaction and was throwing up and wouldn't move to the point where she just laid in her own vomit. I raced to the vet so they could see what was wrong and of course the vaccine was just too much to handle for her size. She shakes like crazy now whenever we go to the vet. The experience definitely made me think twice about how she would be able to handle any procedure.
Ps. Thanks for the advice about the shampoo it has helped a lot! It's become easier to brush and keep tangles out