I danced for most of my life. i am 21. and i often get painful burning, and sharp pains in my left second and third toes. nerve damage?

Possibly.: May be a local problem (ex. Interdigital neuroma), foot problem involving the sole of the foot (ex. Medial plantar neuropathy, tarsal tunnel) or a soft tissue or bony problem (ex. Stress fracture, metatarsalgia, or flexor tendinopathy). There are other things to consider and this should be evaluated by an orthopedist, podiatrist or pm;r doctor.