There are numerous over-the-counter cold remedies that contain multiple medications to tackle the various symptoms that one might have. Many of them will contain acetaminophen or ibuprofen to help relieve pain and inflammation, a decongestant to help with nasal stuffiness, and a cough remedy. As always, you would want to choose the medication based on the symptoms you are experiencing.
However, those who have a history of high blood pressure need to be very careful to avoid cold remedies which contain decongestants.
The most common ones include pseudoephedrine, ephedrine, and phenylephrine. These nasal decongestants work by constricting the blood vessels which can inadvertently raise blood pressure.
One option would be to choose a cold medication specifically designed for those with high blood pressure. One such medication is Corticidin HBP and does not contain a decongestant. Of course, another option for nasal congestion is to use nasal sprays which do not impact blood pressure.
As always, good, old-fashioned recommendations of plenty of rest and plenty of fluids are always a safe bet as well.