To say everyone misses home at first would be a sweeping statement, which just isn't true. Some people cope far better away from home than others. It's that little feeling of anxiousness of being away from that security you had back home.
Sounds like you need to make some friends you can stay in with, rather than finding people to go out with. You don't have to want to go out partying every night, it's acceptable to just stay in, but make the effort with your flat mates if you can to go out now and again if you can tolerate the nights out.