I understand how frustrating this kind of “help” can be, yet I believe this may be an opportunity to get the communication and your mom’s needs aligned. I would do two things. Explain to your mom that you understand how she wants to help and that there needs to be a better way for that to happen for both of you. Explain to her that you believe she is right—that both of you need a professional opinion and a way to move your communication forward.
I would set up a joint appointment with the pediatrician and have the pediatrician render an opinion of what normal is. Your mother is likely to respect what the doctor says, and both of you get to plead your case. If the cough is something that the doctor thinks is a concern, then you have a chance to negotiate with your mom how to deal with things in the future. If the cough is a normal part of being a kid, then you get to negotiate with your mom about future conversations.
Use the physician as an intermediary as you might a counselor. Both of you are trying to do the right thing out of love and concern. Let’s see if there is a way to do this with less wear and tear.