I think the bottom line is, without another reference or transfer standard (i.e. another capacitance meter of known good calibration, or capacitor of known value) on hand, you can't be certain where the issue lays. Particularly if these 'countless' 103 capacitors are all from the same source/batch - they could all be out of spec, or at least, have a very broad tolerance.
Also, just to be clear, when you are activating the relative measurement mode you do have the probes shorted together first? And how are you probing? It makes a difference. Do you have a tweezer type probe, or are you trying to make good contact with surface mount components using regular probes? Are you measuring them in, or out of circuit?
If it were me, I'd acquire some known good, 'low' tolerance film capacitors (1%) from the likes of Digikey or Mouser, in a range of values across the measuring range(s) of your multimeter, and test those. Use through hole components, as they are far easier to make a good connection with, using probe leads with croc clips.
Obviously, this doesn't constitute anything like a proper, full calibration, but it is a good sanity check.