Don't feel too guilty, you reacted out of frustration and pain. It's understandable, and you know it wasn't the best response so don't punish yourself too much.
Dominance theory is about 40 years debunked (at least in the scientific and behavioral community). Dogs do not behave like wolves and wolves do not behave the way dominance theory says they should, so it's a bit like basing your understanding of human behavior on the fictionalized behavior of chimpanzees.
Regardless, thinking this way is setting you up for an unnecessarily antagonistic relationship with your pup. People often equate aggression with 'dominance,' but in reality the more confident a dog is, the less likely it is that it will become aggressive. Aggression is a distancing signal, and it is the mark of a more insecure or fearful dog. This is a dog that will respond very poorly to any kind of correction or intimidation, because it teaches them that their fear was justified. They were put into a situation that they felt was unsafe, then more bad things happened.
Lose the idea of 'winning,' this is a human moral-ism. Fear biting is an escalation of a dog's more polite attempts to tell you to back off because they are uncomfortable or scared. Usually, there are a lot more signals that precurs this (check out the Calming Signals sticky
) but either you're not used to looking for them yet or (being a rescue) the dog may very well have learned that more polite signals didn't stop things they didn't want.
Based on her behavior, it seems very likely that she was given collar corrections and has become fearful of having her collar grabbed (this is VERY common in rescue dogs). Kmes was bang on with those video suggestions, and if you're into some reading I would add the book 'Click to Calm' as a recommendation.
Many small dogs are extra sensitive to handling because it's much more likely for them to be grabbed and physically manipulated against their will simply by virtue of their size. Be careful to let her initiate all physical contact (this goes double for guests, the old 'no talk, no touch, no eye contact' until she makes the first moves), don't flood her (always take new things in small steps), counter-condition to things she is nervous of, and if you have to manipulate her (in an emergency) have her drag a light line or keep her leash on at all times so that you can pick that up instead of her collar. Physical manipulation in training (called molding) isn't very effective. Dog's learn best when they have to use their own brains to problem solve.
Oh, the muzzle. I understand it's important to keep others safe, but muzzles often make fearful dogs more fearful because it makes them even more vulnerable. I would try to fade it as soon as possible.