Work/ life balance dilenma, what should I do?

I'm a contractor who works at a Help Desk every day from 3-10PM except Tuesdays and Wednesdays.

I suffer from depression and have no support system in real life. I have online friends who I enjoy being around a lot but I'm still depressed and I feel like if I could hang out with other people in real life and do stuff together, my depression would lessen.

Most people have weekends off and that would be the ideal time to have off so I can meet new people and make new friends but I don't have it off.

I've tried to ask for Saturday and Sunday off and emphasized that I could work any time on those days, however I got told no because "The data shows that I'm needed to work on the weekends".

I was told that my request would be kept in mind for when a opening for a weekly schedule was available but I have no idea how long it would be until I got that.

I dunno if I should keep trying to find another job or stick with this one until I can get the week schedule I want. The time is the only thing I really don't like. Everything else, I can deal with.

I am freaking tired of being depressed and now feeling cut off from peers. I want to live a happy life but I'm so lonely . .. .

I have certs but no degree so finding a job has been a bit challenging.

Thank you for your help.