Future continuous is better with action verbs. Feeling is a stative verb. The first sentence is better because it uses the cause and effect conditional clearly. If you want to be set a time limit, you can say "If you take this medicine, you will feel better for (time) 2 hours." Or if you want to say the medicine won't fix everything, you can say "If you take this medicine, you will start to feel better". The start implies it will help a little but not cure it all.

What is the correct answer to say You will be feeling better or you will feel better