I am studying music right now, and my mum told me that I am embarrassing her and she doesn't know what to tell relatives whenever relatives ask about me because I am studying a useless degree when everybody around me has already started working at my age and she said I should go work full-time.
I currently have a casual job but in my mum's eyes this isn't considered a real job, and she wants me to go find a real full-time office job.
Well, to stop right here: This is not about your "mom being embarrassed," this is about you doing stuff with your life that will enable you to live contentedly and happily and productively. This isn't about her, IOW. She might not be ready to accept that, but if she continues, you at least need to understand that she's being self-absorbed and worried more about her own discomfort than about what is best for you, so that you can stay "on target" and not let her drag you down.
Things get a little hairier if you are living with her and/or she is supporting your degree in some way, so at that point some negotiation is necessary. But emotionally it's very clear she's not thinking about you overtly, she is consciously focused on herself (although I also suspect she might worry underneath about how you'll make a living, etc.)
So I was thinking of going to work full-time and continue studying music at the same time, I refused to give up on music because I've already come so far and giving up now would be a waste of my previous efforts.
How much longer do you have?
My ideal career though, is I am planning to work for myself. And I already have a few ideas in mind, and I am planning to put my ideas into action. The only problem is, if I try out this self-employment route, I will need time to meet my customers.
But how am I supposed to squeeze in time to meet customers if I have a full-time job + studying at the same time?
Be practical, be Te about it.
Put all the stuff on the table, be realistic, and see what combinations work and what combinations do not.
Maybe you CAN'T work full-time right now to make Mom happy + study + do self-employment. Maybe you can. But you have to be brutally honest and also give yourself time in that schedule to take care of yourself (i.e., not run yourself into the ground / get stressed).
I also suspect that if you can come up with a plan, even if it's not everything your mom wants, if it's a plan that can be quantified so that she can understand it and see a timeline in place, she might ease up since she'll be able to see how it works + be able to tell the relatives something. But primarily the plan is for you so you don't lose your way and know what your goals are and where you are trying to go.
.... as far as music goes, realistically, yeah performance is a hard business to excel in due to the glut of talented people all vying for the same slots/attention. But I will also say that one of my dreams was becoming a professional musician and I have some real talent there, it's just I did not get the support I needed from my parents in a sense that would help me succeed. My father specifically was the voice of "reason" and told me to get a technical job and do music in my spare time, and that made sense at the time; but now I regret it -- I've spent 25 years in a career I'm decent at but don't care enough about to excel, I make too good a salary to just quit because I need to support my children, I don't have the energy to pursue music in my "spare time," and I missed a lot of opportunities to improve my musical skills and maybe achieve some level of success in my life.
I can't provide you a blanket statement to tell you what to do, but regardless of what you're interested in, I do think it's important to honor what your spirit is driving you towards even if your brain can point out a darker realism. Be realistic, but also understand what you need to thrive. The reality is that I would likely have less money nowadays but there's a decent chance I would be a lot happier.