Hello -
This sounds like a fairly typical viral infection that's found a home in the upper respiratory tract. The thick, tenacious mucous being brought up is usually an exudate that forms in the back of the pharynx, and so long as a bacterial superinfection doesn't develop this should run its natural course in around a week's time. The Augmentin should prevent or knock down any opportunistic bacterial infection, but the viral infection, if that's what it is (certainly sounds like it) will simply have to run its course, as there is very little that can be done to resolve viral things.
Dengue
fever would be accompanied by a rash and excruciating joint
pain (this the nickname "bonecrusher disease"). This doesn't sound like that, at least so far, although it could be a mild case. In any event dengue
fever usually runs a course of about seven days anyway. It is usually diagnosed based on the clinical picture (high
fever, severe
headache, the characteristic joint pains, disabling dizziness, etc., plus a postive "tourniquet test", in which a constricting band is applied to an extremity and this causes spontaneous bleeding or brusing in the extremity, and via lab tests yielding a very high red cell count. This doesn't seem to be the case either.
Most any
fever, bacterial or viral, tends to fluctuate regularly, peaking in the afternoon and again during the night. This is classic for most any febrile disease.
Hopefully by now your friend has recovered or is at least feeling better. I hope this is helpful to you.