There are quite a few possibilities.
1. Heart related - chest pain can be a sign of heart attack, although heart is in the left chest cavity, some people can feel pain on the right side as a sign of heart attack. Do you have any of these, anxiety, shortness of breath, sweating, arm and/or jaw pain? If the pain gets more severe in hours you should go to ER nevertheless.
2. Stomach related - it can be GERD(acid reflux), or stomach ulcer. However, sometimes a heart attack can come with vomitting and nausea.
3. Pleural inflammation - is caused by infection, injury, or a blood clot. It presents severe pain in the right side of the chest while breathing or coughing.
4. Lung disease - do you have cough, shortness of breath?
5. Liver disease - it's more like a dull pain
6. Injury - injury to the muscle and tissues there
It's hard to tell you which one is more likely, since the information you provided is very limited. Hope the above can help a little bit.
Last but not least, if you feel uncomfortable to an extent that you think you need to go to ER, trust your instinct.