It definitely sounds to me like the tampon is not inserted properly. I can't tell you exactly what's going on, but the only time I find them really uncomfortable, is when I don't get it in just right.
I have 2 suggestions:
**Go to your gynecologist and let them insert one for you to see that there is no reason they can't go into you properly (no medical issues), and to coach you on inserting it properly yourself. This might be a little embarrassing, but they see it all... this would be no big deal to them... and worth it for you, if they can get you on the right track. There really is no reason a tampon should be uncomfortable if inserted properly. You shouldn't even feel it in.
**Try the Instead Softcup. You can get them at pretty much any drug store/pharmacy (Walgreens, Target, etc.) They take a little getting used to, so I'd practice ahead of time, while you're not on your period, to get used to inserting/removing them. They are VERY different than tampons. They don't even really go in the same spot tampons do, so you may have a much better time with them. The only thing is that you really can't be squeamish about putting your finger(s) into your vagina, because you have to to get it into place, and to pull it out. And removing it is a tiny bit messy, but really no big deal, just something to get used to. The upside to the Instead Softcup is that you can leave it in for up to 12 hours with no leaking and no risk of toxic shock, like with tampons, so it's ideal for an indoor waterpark (Great Wolf Lodge, by chance? We go there and love it...) It looks like a silicone ring (like a livestrong bracelet) that has a thin, clear (like saran wrap) cup attached to it. If you follow the directions to a T, it will pop right into place, right behind your pubic bone. And you will not feel it when it's in. You can even have sex with it in with no mess. I've tried that, and I couldn't tell it was in, and neither could my fiance. And I've never experienced a leak, unlike tampons, where I often wear a pad for the frequent leaks.
As for going without anything, well, I don't think I'd try that... not at an indoor waterpark. You will not be going from locker room, to pool, to locker room. You will be walking all over the place, up and down steps, on and off slides, in and out of the pool, etc. You will need protection, or you will have a mess on your hands. And I would not want to be coming off a slide with blood dripping down my legs.
Go get the Instead Softcup, and try it now. Get used to inserting/removing it while you're not on your period, and don't have the mess part to deal with. If you decide to try this, and have any trouble, message me. I'll talk you through it! :) Truly, if you really read and pay attention to what the directions say as far as the angle of insertion, etc., and do exactly what they say, you will not have a problem.
Best wishes and have a blast!!! We're going to Great Wolf Lodge in January for my son's birthday... Can't wait!!!