Besides what everyone else has recommended, I suggest you not eat a banana. Substitute it with something else.
Also, if you dont like the gym, why dont you walk 2 miles a day atleast 5 days a week? Power-walking at a rapid pace. Eventually you will want to jog some of it.
You should start seeing results within a month. If you want to weigh yourself, weigh yourself every 10 days to two weeks so as not to get discouraged. Insha'Allah things will be fine.
Regarding the comments you get, I say you stand up for yourself. If you saw another person saying those things to one of your relatives, you would probably want to say something to them, so I recommend you say something politely to those who make fun of you. Tell them if they dont like your weight, why dont they come walking with you during your workout to offer support.