With "a"? It´s ok?
I have a backache.

I have a back pain.

It´s ok?- She has a tooth pain. I have toothache.

I don´t understand why I have toothache is without "a".

Question

With "a"? It´s ok?
I have a backache.

I have a back pain.

It´s ok?- She has a tooth pain. I have toothache.

I don´t understand why I have toothache is without "a".

Answer

"I have a backache." This is correct. It is similar to, "I have a headache."

"I have a back pain." This is not standard English. We would say, "I have (a) pain in my back." This means that right now I have (a) pain in my back.

"I have back pain." This means that I often or chronically have pain in my back.