What does a heavily coated yellow tongue mean I recently had a sinus infection and was treated with amoxicilin

Antibiotic. Antibiotic treatment can alter the balance of bacteria and other organisms in the body. In the mouth, this can lead to an increase in the growth of some organisms that may be pigmented, leading to white, yellow, brown or black discoloration. Maintaining good oral hygiene, and gently brushing the tongue can help the tongue regain its normal bacterial balance and color.
Illness. The tongue usually is an excellent indicator of health and the coating is related to your sinu s infection most probably.
Possible yeast. Occasionally antibiotics can have the side effect of causing a secondary fungal (yeast) infection. If the coating wipes off and there are reddish/bleeding spots, this is a sign of thrush (yeast). This may not be the cause however and I suggest you call the M.D. Who prescribed the Amoxicillin and inquire.