Is it possible I have too short a vagina for tampons?

Unlikely/possible. There are some women born with abnormalities in the formation of their internal structures. If someone has had a normal puberty/ menses and sex life but can't use tampons the reason would likely be to changes in normal structures over time. An evaluation by a gynecologist would be in order.
Maybe. Get a second opinion. If you did not get the answers you needed, please see someone else that will hopefully give you a better explanation and treatment options.