should I just walk to the bank?

Aight so I am a college bound student but I am taking a three month break before I actually start. I have a job but I don't have a car which is unfortunate because I really do want to hang out my friends, but that's not the point my point is that I have a job and nobody in my house wants to go to the bank to take out a debit card in my name. the closest bank to my house is about a 40-50 minute walk. I'm 18 right now and yeah my mom doesn't trust me enough to have my own bank account even though I should I give her money from my weekly pay. both my mother and my brother have cars. my mom comes out of work at 4on weekdays, and my brother is free on Saturdays. I'm tired of walking around with just cash I want that to be secureespecially having all this money lying around. nobody's really wanted to help me ever which is why I'm not surprised by this, but it is not like if I'm going to take out a credit card and use money that I don't have, like my brother did. I am way more careful about how I spend my money, which is why I can get whatever I want whenever I want it. I just want to be in a situation where I can't use my own money because I don't have enough cash on me even though I could buy the item if I had a debit card.