If he is your dependent, no, you don't need to file a Gift Tax return.
If he is not your dependent and you pay the medical institution directly, no, you don't need to file a Gift Tax return.
If he is not your dependent and you pay your son, then he pays the medical institution, yes, you may need to file a Gift Tax return (if you or your son are married, you may be able to avoid that). No Gift Tax will be owed unless you have given about $6,000,000 away during your lifetime.
