I’m writing this letter because I’ve been feeling so sick since yesterday and I don’t know what’s happening to me. I’ve got a very sore throat and I can’t breathe very well because of that. At the moment, my body temperature is 39.5 degrees Celsius and I’ve got (or "I have" for American English) a terrible headache and earache. I think it is the flu but I'm not sure. So Doctor House, Can you tell me what my problem IS and what I have to do to feel better?
"I've been feeling" seria gramaticalmente correto para este caso, já que a ação não acabou ainda ou é muito recente.
"Can you tell me what my problem IS" seria gramaticalmente certo porque é uma INDIRECT QUESTION.