Yes, I believe the right test can differentiate between the different antibody responses, telling you if you reacted to the virus, reacted to the vaccine, or both. I looked into this at one time and think I found one that cost $220. Sorry I don not have the link handy.
Get an antibody test that's for something other than the spike. If the vaccine you got only has the spike (all EUA/BLA in the US) the vaccine won't boost anything else.