I was in a car accident about a month ago. when the impact hit my seat belt cut into my chest. i'm still having chest pain when i move. is this normal?

Probably: Were you transported to the emergency department? Do you remember getting any xrays? Even if you were evaluated and imaged (and told everything was negative), it's possible you cracked a rib or pulled a muscle. If you have any trouble breathing, or persistent chest pain at rest, you need to get to an ed and be seen right away. Otherwise call your doctor for follow up (or get one if possible).

See doc: Sounds likely expected- you can cause various intercostal muscle tares, rib "bruising", fractures etc some of which may not readily show up on radiologic studies. As it is primarily with movement it is most likely musculoskeletal in origin, an so will improve with time and anti inflammatory meds like motrin, but you should see your doc to be safe.There are always oddities that doc may need to see.