I see a couple of problems with this plan

First, while they will lock up your bag if you don't claim it, I have no idea how easy/hard it will be to get it early the next morning. I kind of doubt that baggage services will be staffed at 5AM or earlier. So you're going to have to track down someone to open the office and get your bag for you. That will take time and especially in the extremely early hours of the morning may not be possible so you might have to decide between missing your flight and leaving the bag behind.

Second, at some point unclaimed bags get moved from baggage services near the carousel to some other location for processing. I don't know if they "purge" the office each night after the last flights or have some other rule, but you might find that your bag is hard to retrieve especially--again--that early in the morning.

My advise would be the hotel. I don't know that hotels necessarily have policies against 15 year olds checking in. I know I stayed in cheap roadside hotels in TX and the southwest as a 16 or 17 year old on summer road trips to visit friends, but that was quite a while ago so things may have changed since then.

If you can't get a hotel, have to check a bag, and can't check it through then I'd suggest you go ahead and claim your bag and head over to food court outside of security near the International terminal. There's usually enough activity in that vicinity even late/early that you won't be too alone and you might find some other international travelers camped out over there waiting for check-in or security to re-open in the morning.