My 10 month old caught my cough, is there anything I can do to help it? Should I be worried?

Cold/something else. There are a lot of reasons a child can cough. Yes it may be that you had a cold and the child caught it. Colds are caused by viruses and there is nothing that you can take to get rid of a virus like that. If there is a high fever, productive cough, or the child is having trouble breathing you need to get them to their doctor asap. If it is just a cold time will heal all.