First off, it's best to stay away from anything that has aspirin in it. Generally the ONLY pain reliever I use is Tylenol.
Generally most cardiologists will advise patients to steer clear of medications with something called pseudoephedrine in it such as pretty much all common cold remedies on the store shelf... Oy.
The safe list is nice and short:
Robutussin DM
Coricidin HBP
Robutussin has been around for years and there are a few "knock off" brands that are usually just as effective. It doesn't contain psuedoephedrine.
Coricidin HBP is specifically marketed for people with high blood pressure (the "HBP" part) and or hypertension. You have to be a little careful because there are other medicines under the Coricidin brand that have the "evil" pseudoephedrine in it.
And since I know you're asking yourself...
Pseudoephedrine is a wonderful sinus decongestant that has the unfortunate side-effect of making your heart race pretty much out of control for as long as the medication is in your system. While most healthy people tolerate this fairly well, anyone that has a heart condition (or diabetes, thyroid disease, stomach, and/or prostate concerns) should probably avoid it.
I used to be a staunch proponent of NyQuil before my heart started acting up. It was great stuff that essentially cleared away all the symptoms I had and let me go through the day as if I never caught a cold. Then my doctor warned me away from it and I haven't touched the stuff since, as much as I've wanted to now and then....
By the way, the root name, ephedrine, is what killed off a number of college and high school atheletes a few years ago before it was banned from the face of the Earth by a few states. It's a strong stimulant that was used a lot as a performance enhancing drug. It was also used for dieting, speeding up metabolism, and a few other things. The pseudoephedrine is a slightly tamer cousin, it hasn't killed anyone (heart healthy at least) yet, but it's not somehting to mess with either.
A lot of places keep Coricidin HBP behind the pharmacist's counter now because some enterprizing amatuer chemist discovered you could "boil it down" to make LSD, or something to that effect. It was getting stolen a lot from drug stores until they figured out why.
I've been suffering through a cold now for a few days. A fair amount of tea, Coricidin, and occassionally Robutussin (when I'm really desperate) have been keeping me going so far.
I'll also admit to an old fashioned remedy on rare occassion (when I'm beyond desperation...):
A half a shot of whiskey.