E.P.
Yes, it very well can be from a tampon, especially if it was the first time she ever used one. She needs to practice using one when it is not her period. She was probably tensed-up and anxious to get it inserted correctly and it probably wasn't inserted properly.
When she DOESN'T have her period, have her practice. She'll go through a few for practice. The insert will give her a picture of how to insert it. She can use a little lubricant (when practicing) if she is dry. If it is inserted properly, she will not feel it at all. Kotex (purple package - I think is the regular) is really easy to use for a young girl.
As far as going to the Gyne - different issue. Are you thinking that she needs to go for this issue? Using a little lubricant will make the irritation go away - even using a little vaseline for a day or two. As far as tools at the dr., just the act itself of the exam may be a bit embarrassing for her but I don't think there should be any cause for concern about the dr. using the tools. Sometimes there is a little spotting after the exam and the more relaxed she can be, the easier the exam. Any good dr. will be thoughtful to a nervous patient and help them relax - perhaps a female gyne, for her first visit, may be preferable. Good luck.