How do I treat an ear ache due to having a cold in a 10 year old?

Warm compresses. Try putting warm compresses (microwaved damp washcloth) on the ear, and have the child lay on that side.
Earache treatment. At home remedies include warm (not hot) mineral oil for soothing, over-the-counter Ibuprofen (2-3 tablets up to 3 times a day, depending on the child's size). An additional home treatment can be purchased otc --benzocaine drops (e.g., auralgan), a numbing agent. In most cases antibiotics aren't necessary. Currently many experts recommend withholding antibiotics for 48 hours to see if it can heal.