I think the idea of "supporting yourself on your own" is kind of flawed. We're social creatures. We *NEED* community to survive. There's no shame in receiving help when you need it.
If you want to pitch in more, there are plenty of things to do besides making money. Gardening might be a good place to start. I like it; it gets me outside, helps to offset the cost of groceries, and keeps me busy. I don't know what problems you're dealing with, so, if that's not an option, you could also volunteer your time with any sort of group.
As far as taking VA disability goes... As long as we're being robbed at gunpoint, there is no nobler cause for that money than trying to make reparations for the other awful things that have been done it. I do agree that a noble cause, such as supporting disabled veterans, is not a legitimate reason to rob people, but, since it's happening already, we should be working to ensure that money goes towards fulfilling legitimate contracts the government has entered into on our behalf.