Hi & Welcome.
It is not safe to take Ibuprofen instead of Aleve.
You seem to have developed an
allergic reaction ("angioedema") after taking Aleve (Naproxen).
Since both Aleve and Ibuprofen are non-steroidal anti-inflammatory drugs (NSAIDs) which are commonly prescribed to reduce the pain and inflammatory swelling, however there is a high risk of adverse effects like
stomach upset, acidity, ulcer and allergic reactions such as angioedema.
Since both have a tendency to cause angioedema hence it is not advisable to take Ibuprofen for the treatment of oesophagus swelling.
For the treatment of angioedema you need to take oral antihistamines such as Cetrizine or Loratadine.
You seem to be suffering from
gastroesophageal reflux disease (GERD) that could be responsible for the the swelling.
It can be treated by taking
proton pump inhibitors like
Pantoprazole once daily one hour before the breakfast for at least 1-2 weeks.
Hope these answer your queries.