That is NO fun! At the end of your period, the hormones for your next cycle are just ramping up, and I suspect your vagina is a little dry. Without the heavier flow from your period and the hormones of the new cycle still not high enough to lubricate your vagina, you will be dry down there and it can feel like your vagina is burning. It shouldn’t last more than a day or two, and then you’ll feel back to normal.
There are a couple different things that could cause this, and since I have no business diagnosing anything, I’m going to suggest that you schedule an appointment with your healthcare practitioner. If it were me or my daughter, I would be on the phone making an appointment, especially if it’s been a continuous thing. There’s no reason to continue feeling uncomfortable. Be sure to read Dr. Molly’s answer. I’m sure she can point you in the right direction and put your mind at ease.
Ouch! Burning is never a good feeling to have, whether you’re sexually active or not. I think it would be best for you to talk to your healthcare professional and have it checked out. You shouldn’t have to suffer, and she’ll be able to help you stop that burning feeling quick!