Recently started crossfit (intense exercise/ heavy weights). Last 2 weeks, have deep, intermittent chest soreness right side only. What should I do?

Stop CrossFit. If pain persists, see md. If pain resolves, then can resume crossfit with lower weights.
Rest the Chest. It sounds like you have a classic case of overuse syndrome. From what you describe this exercise regimen sounds very intense. Unilateral pain, that varies with respirations or position (hence intermittent), may represent a joint inflammation in the chest wall. Specifically the costochondral joint on that side. Pain along the sternum where it meets the ribs can be iced daily & rest a few weeks.