There is also a trial work period (9months) where you can attempt to work and no income restrictions. It's a way to test the waters and see if you are capable of working. Social Security and the VA have vocational rehab programs available.
Not sure anyone ever answered your question, you may be eligible for SSDI ( NOT SSI) but if you are you cannot work gainful employment long explanation short means you cannot make over the poverty line at a part time less than 32hr a week job.
Don't stay at home and do nothing. Get involved with your local veteran groups like WWP, VFW, DAV, American Legion. They pay the way for most activities including travel to many destinations across the US. It's great fellowship and you end up helping other veterans who are going through the process like you did.