I have had a post nasal drip for a few months. It has gotten better but an ENT dr. Wants me to do a barium swallow do I really need this?

No. A barium swallow is for difficulty or abnormalities with swallowing. If you had post nasal drip which has resolved, and you do not have swallowing problems, then a barium swallow woud not be useful. You should return to your ENT to discuss this further, in case there is more going on that your ENT is concerned about.
Probably. Without a lot of information, i would suppose that your ENT thinks the symptoms are from acid reflux and is checking for it.