Piercer messed up my piercing and took a small chunk out of my cartilage. Will it heal?

Although cartilage does not heal the skin overlying it will and as long as the missing piece is not along the edge of your ear you have a fairly low chance of having any sort of noticeable deformity once it does. Open wounds with exposed cartilage are concerning though because an infection of the cartilage can be very problematic and lead to significant complications. It would be a good idea to see a Plastic Surgeon to have your ear looked at and appropriately treated if required.

I am sorry to hear, I would suggest seeing an ENT or plastic surgeon to rule out a problem as the ear and specifically cartilage is susceptible to infecvtions