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In order to visualize the esophagus then you would need a barium swallow and an upper GI endoscopy. It is unlikely that you would have wheezing with a problem in your esophagus.
I would recommend that you also have lung function tests to explore the wheezing issue.
The ability to perform lung function tests depends on the clinic. If they deal with asthma patients then they will have the equipment.
In terms of your wheeze, this may not be anything to worry about however if it is only heard on forced exhalation and all other tests are normal, then see a ENT doctor for a review as he/she is experienced in narrowing of the throat or vocal cords which may be a factor.