How Long Will It Take To Cure Red Rash Around The Mouth?

Hi, my 18months old son (12.8kg) was just prescribed Flucloxacillin oral solution 125mg, 2.5ml 4x daily. He s been having red rush on his face around his mouth. It started as 1or 2 single spots with white center about 10 days ago and it spreading into red areas with white spots, which are constantly wet as my son is dribbling a lot. He was prescribed Fucidin Cream last friday. We ve been applying this 3xdaily for last 3 days but it s not getting better. My son has asthma and is using Beclometasone inhaler 2x daily. My son also wasn t very well last weak some respiratory viral infection. My question is: How long does it take for the Fucidin cream to start working? And if my son starts taking the Flucloxacillin antibiotics, can he be exposed to the sun as we are going on a beach holiday in 5 days? Many thanks for your answer, S.