Am I a “rising junior” or a “rising sophomore”?

You definitely won't be a junior since you'll still be a sophomore that first semester.

But on the other hand, you won't be technically a rising sophomore. You won't be 'between freshman and sophomore year'. You're still in the middle of your sophomore year.

This is already what you've thought of and why you're asking the question.

The difficulty is being forced into one of these choices by the form.

Since you have to choose, 'rising sophomore' will be less of a lie. You won't be accused of exceeding your qualifications, which is most likely what the results of the questionnaire are being used for.