Heidi, in most cases if you want to shoot NSRA comps you do now have to be a member in your own right. It used to be the case that being a member of an affiliated club was enough, but it's not quite like that now.
I see you shoot from a wheelchair. The NSRA rules allow you to take part against able-bodied shooters on an equal basis, which is good. All you will need is a dispensation. We have a member at our club who is not able to stand and he shoots LSR which is a standing discipline, from a seated position. All we had to do was to describe his "disability" - how I hate calling it that - and to enclose some photos showing how he would shoot from a seated position, without obtaining any advantage. Almost by return of post he had a dispensation letter. The photos are there so that an independent RO could check at any time that he was complying with his permission.
It may be that your local county SBRA runs its own competitions, and in many cases you can enter those comps without being an NSRA member, and if you are entering as an individual it may not be necessary even for your own club to affiliate.
If you were thinking of FT and HFT, it raises the question of which grounds are wheelchair-friendly. That's probably also weather-dependent. Our range is fine in dry weather but soon gets a bit soft in places when it's wet. FT has an open class where there are no compulsory standers and kneelers. I don't know about HFT.