One thing you can do is insert your fingers into your private part and open your pelvis up as much as possible. See if you can feel the tampon and pull it out. You can also try putting water into your private part, that way the tampon itself, will lose its fibers and make the tampon easier to pull out. If that doesn't work, then you will need to go to a doctor and get a pelvic exam in order for them to get it out. Do not worry that much though.
I never used tampons. They don't even reduce your flow. They are the same as pads, just two different things. I find pads quicker and easier to use, plus you don't have to worry about the tampon getting stuck up your private part.
It's going to be grosser than normal. Use your stomach muscles to push down like you're going to go number 2, then you'll need to put both fingers up there to grab and pull it out. It'll come out. There's really just not that far it can go.