I had a mucocele cyst pop under my skin in my lip and now the left side of my lip is swollen should i go to the emergency room to have them drain it?

I would consider a urgent care center or your doctors office. In an ER you would be seen last, in back of car crashes/heart attacks and gunshot wounds, etc. that are considered emergencies.

That's like swatting a fly with a tree branch. An ER visit is expensive. For a more moderate cost, see hour General Dentist or an Oral Surgeon. Or just wait a few days and it will probably go down on its own.