Your sentence is not right. You should say: If before a lunch, I feel hungry, then after lunch I feel sleepy. But fight with means battle, but do not have any same meaning as" feel". Hope can help you, thank you.

"Is this sentence in English correct?" (Your own question was very messy - this is all you need!) :) It looks fine to me to use "fight" in a figurative sense. "If I fight with hunger before lunch, I fight with sleep after." This is a zero conditional, meaning this always happens. If you use a past tense in the "if" clause, you have a second conditional - possible in practice, but not likely to happen. "If I fought with hunger before lunch, I would fight with sleep after." This tells me that you don't actually have this problem! You're just imagining it. Still the use of "fight" here sounds very deliberate, so I'd write it like this: "If I were to fight with hunger before lunch, I would fight with sleep after."

I don't think you intend to use conditional. It must be a general statement. Also, you want to emphasize on the fact that you after lunch although you dont have to deal with hunger, there is always that sleepy feeling to deal with. Then you can write "If its HUNGER that I have to fight with before lunch, it is SLEEP that I have to fight with after" If you want to use conditionals or if you mean it any other way, Peachey has the perfect answer.