You don't need your military records. They will pull them and review what they need. Your receipts won't count as evidence, except that they give them the who, what, where, and when the test was done, so they can request those records on your behalf.
Both the VA and Social Security conduct follow-up exams every few years for the initial phase of a new disability claim. That is to determine if the disability is changing or permanent. It isn't about spying on anyone. Once a disability has existed for 5 years or so, it is considered permanent, and there are no further exams.
If you call the County Administration Office or look them up online, they can give you the VSO office's phone number. Make an appointment and go see them. The VSO will look at what you have and make copies to submit, or will note the information of which records to request. They can advise you further about what else they might need. If you have your DD-214 (Discharge papers), bring them with you.
It never hurts to ask. And you could start receiving compensation and back pay. You have nothing to lose by trying, and everything to gain.