How long can I wait with difficulty breathing and fever to see if it goes away without seeing a doctor?

Difficulty breathing. There are 3 basic symptoms for which you should never wait to see if they go away without being evaluated--shortness of breath, chest pain, and severe abdominal pain. The reason for this is that all of these can be associated with catastrophic illness (as well as many more benign illnesses). But there is no way you can tell. You need an md/do evaluation. See a doctor.
Dont wait. I would not wait any longer, looks like you need professional diagnosis and treatment.