This is a frequently asked question, but it is difficult to answer. The fact is that because our noses only have a limited number of ways to tell us something is wrong it is often hard to tell which thing is causing the symptoms. Both allergies and colds make our noses run usually with a clear watery discharge. Both cause itching, sneezing and congestion. Both make us feel bad.
Despite these similarities there are a few things that can help you tell them apart. Colds are caused by infectious organisms called viruses. Consequently they will sometimes cause a fever (temperature > 100° F). They may also cause additional systemic symptoms such as muscle or joint aches and pains. Allergies are caused by pollen, molds and dander. As a result, people will often have very persistent or recurrent symptoms over weeks with allergies, while colds are usually self limited to 5-7 days.
Unfortunately, there is nothing that says you only can have one or the other and most people who have allergies will also have colds sometimes. In fact, because allergies make the lining of the nose less effective as a barrier against infection, people with allergies often have more infections than people without allergies.
The only way to be sure is to see an allergy doctor and to be tested for allergies.