We were missionaries far from home for eight years, transplanted from Canada's four seasons to perpetual summer, and I well recall those longings to be home with beloved ones in familiar surroundings. Be encouraged and comforted; God knows the longings of your heart and holds you close as you sacrificially serve Him where He's placed you for now.
Home, like hope, is a hard thing to pin a definition on. Nonetheless, I will pray for you. Homesickness is never fun. May God bless you where you are at.