Yes, you can.
Dayquil is a popular cough medicine sold in the US and elsewhere, with active ingredients acetaminophen, dextromethorphan, and phenylephrine. Notably, and to the mild frustration of some travellers with a cold, it’s not available in Iceland.
You are, however, allowed to travel with a personal supply of Dayquil or equivalent cough medicine, with a supply of no more than 30 days of doses for personal use.
If you’re in Iceland with a cold and don’t have access to Dayquil, then your best bet at the pharmacy will be paracetamol (also known as acetaminophen), a common medicine for mild fever and pain, available under different brand names.
There is, of course, one sure cure for the common cold: time and rest!