For most Torah holidays, we keep two days outside Israel out of doubt.
Tu bishvat is a day with Biblical effects (though I wouldn't go so far as to say it's a Biblical "holiday", or a Rabbinic one either for that matter): it affects the Torah laws of maaser and orlah.
However, these laws are only in full force in Israel. Orlah applies mideoraisa everywhere due to a halacha lemoshe misinai, but is permitted outside Israel in a case of doubt, so it would probably be permitted on the 16th of Shevat. Maaser applies in a few places outside Israel, but in those places it's only Rabbinic, so I would guess that we would be lenient for the doubtful day (I may be wrong).
Are there any effects outside Israel of "the second day of Tu Bishvat"?