Hi welcome to Health care magic forum. At present your child is having trachio bronchitis. It Is an allergic manifestation causing running nose, dyspnoea, cough and fever or some of them. It usually is cured by it self completely by the age of about 4years. But upto that time you should be care full and take immediate steps to treat the conditions. after some time it may need nebulizer, and steroids for relief. baby will be playing immediately after relief. But don't worry these are all temporary and have complete relief. Vomitings may be secondary to the cough, or due to indigestion . don't use the words like G.E.R.D.
Besides i advise some diet recomendations for the nursing mother, as avoid taking brinjal, fish, other sea foods, cool drinks, ice water, fruits and juices.
Take more of green leafy vegetables, pulses, sprouts, milk, egg, meat, and dry fruits to build resistance to the mother and child. Wishing for a quick recovery and thank you for calling.