Can Droopy Eyelid Caused by Nerve Injury Recover by Itself?

I find it hard to believe that your droopy eyelid is in any way related to your recent dental work.

My suggestion is that you see a physician to further diagnose your situation and recommend treatment if necessary.

The oculomotor nerve and sympathetic nervous system both provide innervation to the eye that keeps the eyelid open. Therefor any injury to these nerves can result in eyelid droopiness. It is possible that nerve blocks may have induced the observed nerve injury. I dont' quite understand the timing of the injury and this is an important aspect of providing you with advice. In any event it is likeley that the injury will resolve over time.

It sounds like you had a bells palsy. This is coincidental in relation to the dental work. It can take up to 6 months for a bells palsy to recover and in 15% of patients they do not recover well. See a neuroophthalmologist for this.