Vets and animal people as a rule will be much more sympathetic if they feel your not allowing your human issues to get in the way of your care taking.

Clearly she sucks at people skills, but the worse your cat gets the less sympathetic she will be once you do get to her.
Advice. Ask her for assistance, admitted your struggling to administer his meds. I can guarantee you he is making more of a fuss and making it seem far worse than it is.
He will feed off your anxiety and become afraid before you have even approached him with the needle.
It is your fear that will escalate his.
Ask your vet for clear instructions and if she would help while you administer a shot while she is there. So she can assist with you finding the easiest way to do it.
Explain you don't feel confident and that the cat is suffering as a result.

Holding your hands up in this way takes away any power of criticism she may have.
And if she is a vet worth half her salt she will do what's best for your cat.

I know this all seems like a lot, but I have worked in animal care for decades, keep the focus on the pet, and remember that's what it's about.
I strongly advise you address this asap though, before his condition starts to cause him distress.

Good luck and all the best.