Albie wasnt fussed at all when she was chipped,she didnt mess with the implant site at all . Yes she was sedated because yes it is a rather big needle,but she had to be sedated any way to remove her leg band as it was steel and to remove it fully concious could have resulted in broken bones and bleeding vets .
It does sound like they may have quicked a nail. If they , it will be a bit sensitive, like if you cut your nails too far back, if like me, youve stabbed yourself under your nail with a dog brush
( om a dog groomer, i no longer have a dog)
If you notice it bleeding corn flour or starch if your in the usa will help stop the bleeding .
I was also shocked at how un grippy albie was when i had her nails done, i felt so guilty when she would try and land on my should and slide off, its ok , teeko will soon learn how to adjust. Albie figured it out pretty quickly
I would call your vets and discuss it with them and ask for it to be clear in your notes that her nails are not to be touched unless you have asked for it .