Is it possible to get droopy eye lids from local anesthetic at the dentists office? (Photo)

I have a droopy eye lid that I noticed right after going to the dentist about 12 years ago. She had to give me local anesthetic me a few times because it would not take and I truly believe this caused some nerve damage. The reason I say this is because I noticed the droopiness overnight. I felt something went wrong but left it at that thinking it would change but never did. Now that I am over 50 it is much more noticeable. What can I do to fix correct this? thank you S