I Have A Cold Which Started Three Weeks Ago. One

I have a cold which started three weeks ago. One week ago I was prescribed a Z-pack (and cough medicine with codeine) since I had been sick for two weeks. The Z-Pack had no effect on my cold (as I didn't really think it would). Now my cold and cough is worse and I feel like I am getting a sinus infection. I have a bad headache. I take Losartan for high blood pressure, and my pressure is still higher than it should be. I am not taking a decongestant due to the HBP. The drainage down my throat, the productive cough (now with tiny specks of blood) is making my life miserable! I can't sleep because of the coughing. Cough medicine, even with codeine, does not help. What should I do now? I have a full dose of Cephalexin 500 mg, which I never needed, for a potential infection after dental work. Should I start that? See a doctor? Your advice will be appreciated.