The antibody titre, a test to see if you have antibodies against a number of antigenic molecules that your own immune system used to defeat Covid-19 can be done. It is not a Covid-19 test.
https://en.wikipedia.org/wiki/Antibody_titer.
A Covid-19 test has been created to see if you have RNA from the virus in your blood OR other molecules that are given off by cellular lysing as the virus reproduces and breaks open infected cells (killing them) and releasing infectious virus particles as well as many defective particles (DIPs) and excess functional viral subunits that were also made in the cell but were not used in building a virus. The virus does not have an inventory control mechanism and keeps making virus building particles as well as completed functional viruses as well as partially build particles - until the cell is lysed(broken apart and killed, releasing the whole mess)
There are several tests that look for your titer as well as several Covid-19 tests that look for Covid-19 infection indicators. If you knew the exact test you took, you can read about what it tests for and this may help you.
In theory, if you have antibodies they will resist a future infection by the same virus - the titer fades with time and the rate of fade varies,