4 weeks of antibiotics is a lot. Rashes are the commonest side effect of antibiotics. Discontinue the antibiotics. Any fluid still present in the middle ear should be sterile by now. Get his eardrums examined. If his eardrums are dull or show evidence of fluid / air bubbles get an Impedance Audiometry
(I/A) done. The Eustachian Tube which connects the ear to the nose in an infant is shorter, wider and more horizontal than in an adult. Therefore any infection in the upper airway can easily enter the ears. Ensure that during feeding time, his head is held high and do not feed while lying down. Supportive medication
such as anti allergics, decongestants may help. I hope there is no fever
or antibiotic associated diarrhea
now. Post the results of his examination and I/A here.