We usually don't have sex during my periods but when we have sex just the next day after my periods I have burning sensation in my private part.

Hi there !

That's actually entirely up to you guys as we don't have much details.
I would just say, if it doesn't bother you then go for it.
The only thing is to protect the mattress and also I would advise your partner to wear a condom (just in case), but other than that it's your choice.

I can explain the burning sensation you feel after your period stops, I had the same and it's very easy to get rid of it.
During your menstruation your vagina is flooded by the blood your body is evacuating so everything is "well moisturised" but the use of tampons especially tends to dry the vagina from it's own moisture, so as soon as you're trying to have sex it starts burning because it's very dry.
Try to put lubricant on the inside before starting anything and you should be fine.

Hope I've been able to answer your question...
JD

How old are you?