Why do I have chest pain after I drink?

Esophagus. The details of what type of drink is unclear from your question. But caffeine containing drinks or alcohol can lead to or exacerbate reflux of stomach acid which can irritate the esophagus. Also, some people develop a spasm of the esophagus, essentially a "charley horse", which causes pain. Get it checked by a doctor.
Drink what? Chest pain after drinking alcohol can be from reflux, esophagitis (alcohol increases reflux from stomach); may have esophageal inflammation or ulcer. After any liquid may reflect muscle or nerve abn. Affects peristalsis (coordinated contractions), as well as above. Arguably cardiac causes can do this too. Unlikely pulmonary see your doc, make sure heart is ok firs (if you have risks), check gi.