My 8 month old has a really bad cough and is sick ...

My 8 month old has a really bad cough and is sick for over 3 months. Its Jun back in April she and her 4 year old sister was put on antibiotics. For bronchitis for the both of them and my baby also had a left ear infection. After 10 days my baby looked like she was getting better but still had a cough, my oldest went back to dr and she was still sick and she now had walking phonia. Well they gave the oldest more meds and she got better. Well my 4 month olds cough came back but ten times worse then ever.  So I took her back they said they were not sure whats going on her lungs sounded fine and her ears looked good. She was sent home. Well I have been taking her back and forth for this cough that wont go away and I'm sure it does not help that there is about 6 MD's to the office she goes to so she never gets to see the same one. Well I took her back thur to the dr asking please lets find out whats wrong she coughs all the time and she chokes and she does not sound ok. He put her on antibiocds and wants her to take it for 20 days. Because he thinks that maybe her ear infection didnt clear up all the way. Today is monday and last night I took her to the ER because she got a fever that she never had that was 102.6 and she was vomiting and when she stoped she would just lay on the floor and not realy move just cry a little. Well the ER did blood work and test and checked for UTI and did a X-ray and came up with not one thing. Went to dr office to day she still has a fever and all she wants to do is sleep and she will wake up to cry when her fever is getting high and she will drink her bottle and go right back to bed. Dr is going to send her in to get a CT in the am but my question is does anyone have any idea what she could have?  Is this normal for a baby to get this sick?  Is there other test that can be done? If anyone can help me with some info it would help a lot?  Thank you, for reading my long post.