Poor dear! First, take a deeeeep breath and calm down. Squishy is going to be fine, I am sure.
I cut the tails of two of my larvae (the larvae are about 5 inches long). It is just a cut, and it will heal. If the water is clean and healthy, there shouldn't be a problem. Just keep your eye on the cuts to make sure they don't get infected. Also, it is not unusual for an axolotl to freak out when being moved. Furthermore, it is normal and very common for them to hide behind plants.
You also don't need to take Squishy out of the tank to clean it. Just be slow and gentle while cleaning and she will wait and watch you.
I wonder more about what you mean about Squishy curling up. I don't know if this is unusual - my adults as well as the juveniles like to curl their tails around sometimes. The juveniles do some pretty strange acrobatics, too, including something almost like staring at their own tails, or swimming up the tank and floating slowly downwards. How exactly is she curled up, how long has she been that way?
It could just be that Squishy is new and shy, maybe a little scared. Of the six junveniles I have had in the aquarium for two weeks now, two of them still hide behind plants and I rarely see them at all. Being moved out of the aquarium is only going to add to Squishy's worry.
The best way to tell if something is wrong with your axolotl is to check your water paramters. They are the usual culprits. If the water is good, Squishy is probably fine, too. Maybe you let her be alone in her tank for awhile. If you are trying to hand feed her, it might be better just to drop the food near her without putting your hand in the water, and then go away from the tank again to let her eat in privacy. You know how it is with shy folks. You go have a nice cup of tea or cocoa and relax a bit, too.
-Eva