I got into a bad arugment with my mom and she found out i called her a b***h,now idk what to do??help me pleas?

Ok so me and my mom havent been getting along a LOT lately,like everyday.She get mad over little things and makes them a bigger deal than she should.She acts like its always me and that i make her the bad person.For the past week at least every day(this is not a exaggeration)Ive cried my eyes out. Im 15 and I vented to my friend saying my mom is a B**** and my mom found out now shes hurt,I dont care that much because shes made me cry so much so she deserves to feel a little hurt too.But im not sure what to do I wrote her a letter of apology,but i think shes still upset...HELP!