Feeling homesick at a new school or camp usually means home was good to you. That’s not weakness, that’s luck.

Missing something is proportional to how good it was. Homesickness is unpleasant, and it is also evidence about what you came from, because nobody aches for a place that gave them nothing. Read that way, the feeling stops being proof you cannot cope and becomes information about your luck. It still hurts, and both of those stay true at the same time.

Let yourself miss it without treating the missing as a problem to solve. Call home at a fixed time rather than constantly, since a set point is easier than an open question all day. Then give the new place two more weeks.