You can be both homesick and happy, trust me.
In my career at camp, I have had my bouts of homesickness; I would actually argue that every camp person has, at some time or another, had their own version of this experience. I had them as a camper and not the first time I went off to camp but about the fourth time I set off for a few weeks of sleeping in a tent. I’ve even had the occasional pang as a staff member and the thing about all of it was that I never stopped loving camp while I was pining for my bed at home.
That’s the thing about homesickness that can sometimes be so frustrating and confusing. You aren’t always miserable, you don’t always want to leave; you’re still having fun, you still want to be with your friends. It is not an either or; you can be both homesick and happy. To understand this phenomenon from a much more eloquent source than myself, I encourage you to pick up Michael Thompson’s book Homesick and Happy.