Since October My Nephew Has Been Constantly Sick. He Is

Since October my nephew has been constantly sick. He is 13 months. While my sister and brother in law are at work he goes to a nanny who watches 3 or 4 other children with him. Since October he has been diagnosed with bronchitis, pneumonia, and an ear infection. Since Thursday he has had a temperature of an average of 101. Every time he has been taken to the doctors or the hospital they give him Tylenol or Motrin and send him on his way. Thursday night he was taken to a walk in medical center because he started coughing and wheezing. The cough sounds like he is coughing up fluid but the doctor said he sounded clear. He sent him home with a nebulizer and a prescription for albuterol and pulmicort. He hasn't been able to sleep very well and it does seem that he has a decrease in appetite. We are thinking he may have asthma but could he have an immune deficiency? What should we have his doctor do?