After I eat fruits like avocado, bananas, watermelon and mango it feels like my throat swells and some difficulty with breath. Is it an allergy?

Yes. It is unusual since those are not all related kinds of fruits, depending how you group them (pit/stone vs not, tree vs ground, etc.). Consult an allergist for formal testing as there are likely others and your reactions will likely worsen with subsequent exposures, so you may need an epi-pen.
It may be allergy. It may be due to allergy and i will recommend you consult your doctor or an allergist to get tested for that.It can cause get serious frm the symptoms you are describing. Till then do not eat these fruits.
Sounds possible. Be careful and avoid these foods until u c ur doc.