If I take coricidin cough and cold and I don't have high blood pressure, will it effect me adversely (I'm taking it for the right reason, I'm sick)?

Safe medication. For a young healthy person a short course of over the counter medication is unlikely to be harmful. The other side of that, though, is that most OTC meds aren't very effective. For a serious cough a prescription medication might be best, but if the cough is minor you're better off to try home remedies. Look here for ideas: http://commonsensehome.com/home-remedies-for-coughs/