Frequent cough n cold Hello, my daughter

Hello, my daughter is 10 months old.. sje was exclusively breastfed for 6 months. As i joined work after that, she is 60% on bf, 20% on fm and 20% on solids. In last 4 months, she cought cold 4 times. In last 1 month (we had travel due to family emergency) she cought too much cold(no temp at all) which lasted for 10 days...1 week after that she cought cold again, we took ptoper medicie es as prescribed by pead..nebulizer, vicks all home remedies as well. She was fine for 1 week and cought cold with cough again.. its like for past one month she is having something or the other going on.. she got her 2 teeth in this phase n still she is bity as upper tooth coning.. i am confused why is catching cold so often.. is it some allergy ? Something we r doing wrong? Can someone suggest wat could be d reason and wat can i do to help my baby..