If you are close to your mum you should be able to talk to her...ask her why she thinks he is cocky..and tell her how much you like him and how he makes you feel. Tell her it's unfair that she hasn't given him a chance and ask her to do it for you.
Every parent wants the best for their children...maybe she has heard things about him that she doesn't like..
Ask her to give him a chance...and take it from there. If she sees how happy he makes you she might change her mind. We all want our kids to be happy...but sometimes you can be blinded 'by love' and not see what is blatantly obvious to those who care about you.