Ear infection with puss coming out of my 3 yr olds ear.?

2 days ago I took my 3 year old to the doc because she was telling me it hurt and she had a fever. The doc said it was drainage from her cold and she didnt have an infection. So that night she cried and cried and said her ear hurt so I went back in to the doctors and said, you have to look again...she is up all night and wont let us touch it or anything. So he looked again and said there was a lot of wax in there and it does look a little red. Then he looked again and said there was a cold sore looking thing in there....anyway he gave us antibiotics and ear drops. So when i went to put the drops in I saw a bunch of crusty stuff around her ear and puss coming out. I was amazed that he didnt see this. I am now wondering if he has given her the right antibiotics. How could he mistake puss for earwax???? I dont know if I should put the drops in either??