Top of left arch popped during ballet class followed by mild pain and a burning feeling. pain around the highest point of my arch/big toe metatarsal.

I would : Discontinue any ballet until I saw the foot doctor. Ice the region and make sure to wear a shoe/sneaker with an arch support until you can be evaluated.

Ice, rest, pain meds: The injury during "ballet class' may have caused a sprain or strain in the muscles or tendons in your foot. Acutely, after the injury I would ice the area for 15 -20 minutes several time a day in first 24- 48 hours.I suggest taking either acetaminophen or ibuprofen for the pain. You should have the injury evaluated by your physician in the next 24-48 hours because X-rays may be needed.

May be serious: You may have strained your tarsal-metatarsal joint or may have developed degenerative changes in that area. It would be best to see an orthopedic foot specialist for an evaluation and X-rays.Whenever you hear/ feel a pop,the injury is usually significant. Worse case scenario would be that you sustained a Lisfranc injury or an injury to the mid foot joint complex. Surgery may be recommended.