I'm so sorry that at your young age you have to deal with this...or any other chronic illness!
Certainly it was before your time, but it was one of the Beatles who famously said, "Life happens, when you're making other plans..." Lots of people, especially at your age, figure out their lives..
and then things happen. Things like: Jobs don't work out, natural disasters strike...or like you, a chronic illness happens. And, after a time of anger and grief, you'll find that you go on living, just not quite how you imagined it, but living OK, and doing OK and getting on with your life.
But it will take time. You've had a lot to deal with in a short period of time, and you need to give yourself permission to grieve and be angry..and adjust to your meds. Yes, injecting the Betaseron will get easier in time. I always remind myself that my friend, who has diabetes, uses the same size needle I do, to inject her insulin -- several times a day, not just every-other-night, like me. So I watch her, and then my little injection doesn't seem so awful, most of the time (I've been on Betaseron for 13 or more years, now).
Don't be afraid to talk to your family and friends. If you haven't already, go over to the National Multiple Sclerosis web site, at www.nmss.org and do some reading. There are things there that you can download that can help you explain to your family what you're dealing with. They may well prove to be a valuable source of strength and help for you, as you come to deal with all of this.
And don't hesitate to come back here, and ask questions. We'll try to help.
...I am not a doctor, nor health professional, and don't pretend to be one, here.....