I don't want to get my hair and nails done for my mom's wedding at a salon and just do it myself
Why? Do you not want them to do your hair and nails?
I don't want to let her know that I was cutting my nails in school.
I don't think your mom will be upset about your nail cutting but she will be upset if you do not follow her wishes. Children should follow their parents' wishes when they can.
I don't think she will mind in the end. I have the right to, and she can't stop me.
You're right and if you really think she won't mind, then it is okay to do your own hair and nails, as long as the end result will be appropriate for her wedding. I hope you support her and be with her whenever she needs you on the wedding.