My suggestion would be for you to tell your mom that you want to continue to help her out and that you would be willing to work out a schedule of household responsibilities with her. Keep the schedule posted where you can both see it. Don't agree to do things that you know you are not going to have time to do, given your social life. I think that she will respond positively to this effort and to your letting her know how appreciative you are of the things she does for the family.
If these are true friends, they will also understand your family circumstances and cut you a little slack every now and then to help out a little more at home. My guess is that you have been great at helping out your mom for a long time. You love her and she loves you. You are old enough and mature enough to let this fight pass and to apologize, if necessary for anything you may have said in anger that might have hurt your mom's feelings. You might want to ask her to remember what it was like when she was 15 and how she would feel if she were in your shoes with her friends in this situation. So if you can both put yourself in each other's shoes and think about how you love one another, then I am sure that you can come up with a solution that may not be perfect, but it will be OK. Thanks for writing and let me know how things work out.