Hi HES246! I’m not sure about period-specific burning but it definitely strikes me as possible just because of other period-related pains like cramps and sensitivity. Sometimes it can be easier because there is more lubrication from the blood, but if it’s feeling painful it could be for a couple of reasons. Using more lube is always a good first step, and when starting with a new dilator size there can also be discomfort when moving up. I would recommend going back down a size and getting comfortable with that one again before moving up, or using the smaller one before switching to the larger one in the same dilating session.
Let us know if you have other symptoms – it may have been a one time fluke, but if you think it wasn’t, it’s worth getting looked at by a doctor.