There are several issues here, but all of them are going to depend on the particular laws in the jurisdiction involved.
In many jurisdictions a person hired to perform a service, such as a contractor, must use professionally reasonable skill and care, and failing to do so is a breach of the contract, and may be grounds for a suit. Whether the peeling is due to lack of skill or care depends on specific facts not mentioned in the question.
You may want to get an opinion from a different reliable professional as to what it would cost to correct the problem.
In some jurisdictions a person who is not yet of legal age may cancel a contract. But in many of those a minor who cancels a contract because the person is under age must restore the other party to the situation as it was before the contract, such as by returning purchased goods. In this case that might involve returning a payment.
Moreover, such cancellation (known as "avoidance") is not automatic, the minor must explicitly cancel.
Also, in some jurisdiction a minor providing professional services may not cancel contracts related to those services. This most often comes up in regard to child actors and entertainers, I think.
Since there was no written contract a court would have to determine, as best as it can, what the terms of your agreement were.
Before you can even file a suit you will need to locate the other party, finding at least an address.
In short, there are many factors that might affect if such a suit would be successful. Those cannot be evaluates on this forum. You might be wise to consult a lawyer in your area who you can explain the full details to. The clerk of the relevant court may be able to describe basic court procedures, but probably cannot give legal advice.