There are now so many different type of contraceptives than just the pill. For example, the ring, depo, patch, iud.
Research these other types of contraceptives and talk to your doctor.
Even with the pill, there are some with less hormones.
My doctor stuck me on a pill with the least hormones possible because i'm a small girl.
So I reccommend looking into other methods. Usually changing the type of birth control can help.
I've been told by my boyfriend that condoms do the same thing to him. He says he only feels something if he penetrates really deep.
Condoms can also cause burning or pain for the female too (there is also the female condom if you want to try that)
as far as the burning, you could have a vaginal infection.
Anyways, your doctor can help you find something that works.