Can I give my baby over-the-counter cold medication?

No. Although as parents we want to do everything we can to help our children, cold medicines have not been shown to be beneficial, and are potentially harmful to young children. In fact, over the last several years the government has begun removing these products from the market.
No. You're not supposed to. Otc cold meds aren't supposed to be given until 6 years old, though some pediatricians will cheat down to 4 y. Now, that's the official version, but you may discuss shades of grey with your doctor. Vicks can be used at an early age and has been shown to help with cough. Truthfully, cold medicines have not been shown to alter viral illnesses in duration or severity.
No. Cold preparations are not recommended for children under 6 years of age because the risks outweigh the potential benefits. These include preparations for cough, congestion and runny nose. You can give medicine for pain and/or fever.