How would one create a balanced dragon PC?

I’m running a DnD 5e campaign and had a dragon-born sorcerer with Draconic Bloodline as a sorcerous origin that used the level 9 Wish spell to wish to become a “true dragon.”

Are there any rules about having dragons as PCs? If so, where? If not, how would you go about making it somewhat balanced?

Background

An excerpt from the wish spell:

You might be able to achieve something beyond the scope of the above examples. State your wish to the DM as precisely as possible. The DM has great latitude in ruling what occurs in such an instance; the greater the wish, the greater the likelihood that something goes wrong. This spell might simply fail, the effect you desire might only be partly achieved, or you might suffer some unforeseen consequence as a result of how you worded the wish.

I was considering going with the “the spell failed” option, but decided to have a little fun with it. I warned him about the chance of it going horribly wrong, but he said it would be out of character for his PC to turn down any opportunity no matter the risk.

So I set up a roll table: 00-10 killed him or similar, 11-35 turned him into an egg or against the party or a few other creative things, 36-50 the spell just failed with all of the negative effects of the wish spell gone wrong, 51-80 gave some cosmetic changes, 81-97 adjusted stats a little (can no longer hold weapons an shields but breath weapon is stronger etc.), 98-99 and it actually worked.

Of course he rolled a 99. I gave him exhaustion and said he needed time to recover from the ordeal, but I really need time to figure out what to do with him.