I agree that everybody is in the same boat as you and that it will definitely get better within the next few months. In the meantime keep your door open, say hello to students in the dining hall, and get involved. My daughter was miserable at first… so miserable that I told her to make a list of schools to transfer to. By mid October she was incredibly happy and has been happy ever since. What you are experiencing is normal.
It appears as though there is some happiness beneath the normal feelings of trying to adjust. I agree that the guilt should go… but I recognize that this is much easier said than done. Your happiness and success will make your mom happy, and your friend will adjust.