I'm sure I read this in my scuba book, but I cant find it again.

If you have a cough (I mean coughing ever 2 mins) are you allowed to dive.

I know that you are not allowed to take medicine as it has different affects under water, so is there anything that would help my cough before Sunday (I need to be better or I cant get my Open Water)

I don't think you are allowed, because if there is slime (right word?) blocking any airways, and the expanding air can't get out as you go back to the surface, it could do damage to lungs etc.
Also, if you have a cough, there may be other symptoms of a cold present, such as a blocked up nose. Even a little bit of a cold can cause problems when you want to clear your ears, and if you can't clear them properly, you could damage your hearing.

So ask your instructor about it, but I wouldn't count on it too much.

B.t.w., there are medicines that are allowed for scuba divers, you could try some anti-biotic drug?There are lists available on the Internet on medication that is and isn't allowed for scuba divers.