It is important to understand whether a cold is viral or bacterial. If viral then it will run its course and nothing really will remedy it. If bacterial then it will require medications. However you can get relief from symptoms. Eucalyptus oil can help in breathing easy so just some eucalyptus oil in a diffuser in the child's room. Steam can help with clogged nasal passages. Saline nasal drops are also helpful especially at night to help sleep better. And finally since the child is one year plus can give a tsp of honey with ginger juice and black pepper three to four times a day.