Hello Chetan and welcome to HCM
Yes you surely needs chest X-ray done of your daughter. In addition to X-ray you also needs to check CBC,
Mantoux test, Sputum for AFB to rule out
Pneumonia,
tuberculosis and other respiratory track infections.
The recent loss of apatite and vomits are due to growing teeths and need not to be worry about that.
Fever may or may not be related to growing teeths.
Get your Chest X-ray and other investigation done and consult your doctor.
Please take some precautions:
1. Protect her from changing climate, keep her protected with cloths.
2. Change her cloths immediately after urination or stool. Wet cloths cause
respiratory tract infection more frequently.
3. after every diet take your baby in standing position so regurgitated milk or water does not enter the respiratory tract and causes cough and fever.
More possibility are that you are getting fever and cough due to wet cloths. Precautions are always better than cure.
Best Wishes
Dr. Kulbir