Can I give my 3yrs old OTC meds for cough and cold?

Yes and No. Sometimes yes and sometimes no. Some over the counter medications are not safe for all babies. It is wise to have a discussion with your doctor about which medications you can use for some common problems, and write down the advice. Recheck with followup visits.
No. They do not work. And are not recommended for children under the age of 6 years.