Cold and headache. Far. please suggest.

From past 2-3 months something keeps happening to me. It all started with cold, my ear got blocked due to it. After that, I suffered from fungal infection in my ear. Then again cold affected me. For me it usually takes longer than normal for the cold to last. I visited to an ENT specialist, who suggested some medicines alongwith steam inhalation. From past three days I have headache in the morning. It starts after sometime, when I wake up and happens during morning only, it vanishes itself in the evening. I thought is happening due to incomplete sleep that's why I didn't told my ENT doctor about it. The headache pattern is quite weird. First day, it was in whole head, second day, it was on both sides, and now it is only on the right hand side. I am not sure what is happening to me. Should I go to some general physician or some specialist (in case if yes, then to which one) and have my complete body checkup. I didn't took any medicine for headache so far. Please suggest.