 [ Symptoms ] why do generic drugs make me cough  i take meds for a thyroid condition and blood pressure meds i have tried several different generics the all have caused a constant cough insurance c will not cover the brand names i am paying more than 500 00 per month for my meds [ Disease ] if you have high blood pressure it is usually advised that you avoid cold medicines that contain a decongestant like pseudoephedrine or phenylephrine because they can raise the blood pressure and heart rate in some people your pharmacist can help you choose a cold medicine that will help your symptoms and mix well with your prescription medications