I'd cut out a lot of "bad" foods but it is okay to eat bad foods once in a while.

You're taking the right step. Getting on that bike will make you work - you will sweat and when you arrive at your destination you will realize you are not out of breath anymore. You will feel better about yourself and start doing other things. You shoudl keep at things for more than a month.
I find that eating just egg whites is strange. seems like a waste of food and the yolk is good for you in moderation of course. Should have a healthy portion of veggies, fruits, protein and fat.
You should learn to shop for your own food that is not packaged or frozen. No more lean cuisines or boxed foods that are marked as 'healthy.'
Maybe you can even start your own garden.

Have you also gone to see your doctor as well? Blood tests to check your thyroid, blood sugar, etc.

Good luck.