May I suggest, first of all, that you choose your words carefully. It’s one thing to be “annoyed” (or to use your word, “irritated”) with your mother; we all go through that from time to time in greater or lesser amounts and for long or short periods and for all kinds of reasons. When you say that you “despise” someone, that’s serious dislike to hate. If you start thinking (and saying) that you actually “despise” your mother, then people will assume that you know what the word means, speak to you about her in that way – and you’ll get to that point eventually, if you aren’t already there. And I don’t think that you’re “there”. You’re annoyed with your mother; that’s clear.
Next, and I hope you won’t take this the wrong way, but… your writing reflects your thinking. And I see a lot of disorder, incomplete thoughts (expressed in incomplete sentences), muddled thinking (non sequiturs) and misplaced cause-and-effect, as well as red herrings (what does Mike in Philadelphia have to do with the price of fish?). I’m not saying this to be “the grammar Nazi”; you need to order your thoughts. Calm down. Express your dissatisfaction in complete sentences. Use facts to support your thoughts. Does your mom really “yell at you all the time”? I hardly think so, unless she has a severe mental impairment. And if you think that she does that “all the time”, then maybe you have the mental problem.
So… what sets her off? Surely you know what causes her to be annoyed with you and raise her voice at you. I doubt very much it’s just “because you have a girlfriend”. But if your thoughts of your girlfriend put off all thoughts of household chores and responsibilities, cause you to neglect your homework, fail to relay messages, etc., then she has a right – a duty, even – to try to correct you and get you to focus: First things first. (That was just a ‘for instance’; obviously I don’t know your situation.)
So along with some of the other very good advice above, especially from @marinelife about how to talk calmly and rationally with her, here’s my advice:
1. Choose words carefully when speaking with her and about her. Speak slowly and deliberately and don’t say anything that you don’t mean. (And don’t BE mean.)
2. Order your thoughts. Express them in complete sentences – you won’t believe how much better your thinking gets as your writing improves.
3. Address your mom’s concerns. She is your mother, and she has a responsibility to raise you properly. One of her major concerns, I’m sure, is that she’s not with you as much as she would like to be. Sometimes that concern is expressed in frustration and apparent anger.
4. Be patient. This is probably the most difficult of all, since you feel, I’m sure, that “life is passing me by”. But you have a very long life ahead of you; there’s a lot of life to come, and you don’t need to try to experience it all right now. Your girlfriend can wait if she really has strong and true feelings for you, and if she doesn’t, then there’s no sense in knocking yourself out for her.