What you are describing is so common. Please read this thread: http://talk.qa.collegeconfidential.com/t/to-those-who-feel-lonely-homesick-friendless-think-they-chose-the-wrong-school-etc/
100%, do not go home over the weekend because you are, without realizing it, making your situation worse. Everyone is away from home, and during the week, it’s harder to make friends because of classes. Weekends are for meeting people and making friends. Everyone is doing this every weekend while you are home. So please just grit your teeth and stay at college every weekend.
Lots of people don’t gel with their roommates. My own kid didn’t, no option to come home, so she had to make friends outside of her dorm room. She was very shy and awkward, but got through it, and so can you. You’re in clubs and are chatting to people in classes, so you are off to a good start.
Give yourself time and stop going home. Trust us when we say it isn’t helping. And don’t even think of transferring unless you are sure you’re not going to be tempted to run home when things get tough. Because this is a tough time, and maybe everyone else seems to be having an amazing time, but trust us again, they are all going through a similar experience right now. Hang in there!
P.S. Talk to the RA, that’s what they are there for!