I have that problem, too. I always wear pantyliners, just in case.
Regular Tampex sucks. Go with Tampex Pearl.
Definitely try different varieties, different strengths; everyone is different, as you can see from this thread alone. 
For what it’s worth, I had to wait until I um…wasn’t a virgin anymore…to use a tampon comfortably.* They simply didn’t fit until then, not any size, not any type. Your mileage may vary, but definitely try different types.
*The best part about losing my virginity was finally being able to use tampons 