Can taking augmenting 625mg and metronnidazole 500mg together cause sore throut and drowsy?

Not likely: That is not a common or known side effect of either. I would look to what they were prescribed for or some other explanation. Recommend you finish all antibiotics as prescribed by your doctor unless you discuss it with them first.

Drowsiness: I believe that the drowsiness is more apt to be caused by the condition,presumably infection, for which these antibiotics are prescribed. I am not aware of drowsiness being a side effect of these medications. Throat discomfort may be from infection but I suppose irritation from the antibiotics is possible though unusual. Your pharmacist would be more knowledgeable about medication side effects.

Interaction : No, the combination should not cause problems..However if you are allergic to either of the compounds that could give you symptoms such as drowsiness

Drowsy/Metronidazole: No using these two Antibiotics together will not cause sore throat.But drowsiness is possible with Metronidazole