My 11 month- old has a bad cough and diarrhea but no fever. is it serious?

Needs to be seen: Cough is the body's way to clear out the airway. It can be caused by many reasons. Similarly, diarrhea can be caused by the body's need to get some material, such as an infection, out of the body. Even without a fever, in a child that age i would suggest they see the doctor soon.

Likely viral: Make sure he's getting plenty of fluids to avoid dehydration - pedialyte works well. If any difficulty breathing or fever he should be evaluated.

Viral Illness: May be enterovirus or alike. Starts with upper respiratory symptoms with runny nose, cough, sometimes vomiting, and ends with diarrhea. Give pedialyte 4-6 ounces for each diarrhea, continue if you are breast feeding. Food will be mainly: bananna, rice, applesauce, chicken/soup, crackers. For cough can give Benadryl (diphenhydramine) 4 ml twice daily, use steam inhaler or a vaporiser. If cough worse, see his/her doc.

Possible allergy: I would advise that you see Pediatric Urgent Care to determine if your infant has an allergic reaction. Otherwise these symptoms are probably related to an infection. If the cough disrupts sleep or is associated with vomiting, please see your PCP soon.

See a pediatrician: Any child under a year in age with these symptoms should be seen, if only to check for dehydration. Your pediatrician should be able to reassure you. Good luck.