Homesickness is ordinary, and the year takes longer than anyone admits
Missing home is not a sign you chose wrongly. It is what moving costs, and it is payable in instalments.
Homesickness rarely looks like the word suggests. It is not usually weeping about a house. It is flatness on a Sunday afternoon, irritation with a place for being unfamiliar, a specific longing for a food you cannot get, or the strange grief of a family event happening without you while you sit in a room. It comes in waves rather than a straight line, and it very often arrives late, weeks after the busy arrival period ends and the novelty stops carrying you. Feeling it is not evidence that you made a mistake, and it is not something you have to earn the right to feel by having a hard life.
A few ordinary things reliably help. Keep contact with home regular but bounded, because constant contact can keep you living in the old place rather than settling into this one. Recreate one small ritual from home, whether that is a dish, a walk on a particular day, or a phone call at a set time, so the week has an anchor. Build routine deliberately, because routine is what turns a location into a life. Say it out loud to somebody here. The relief of finding that the person next to you feels the same is genuine and immediate, and it is the reason so much of this issue keeps ending in the same advice: speak first.
Two honest notes to finish on. First, if the flatness stops lifting, or you are not sleeping, or you have stopped doing the things you used to enjoy, that is worth taking to your institution's student support service and to a doctor. We are a magazine and not qualified to advise you on your health, and those are the right doors. Second, the timeline. It commonly takes a couple of terms, sometimes the better part of a year, before a new place feels normal, and it will happen without announcing itself. You are not behind. You are simply partway through something that takes longer than anyone says.