Most particle board cabinets are covered with either a veneer of wood or vinyl.
You mentioned that this is an apartment, which could mean that the cabinets were painted prior to you moving in to make them look fresh and clean.
- The taste of shellac that you are experiencing may be off gassing from the paint which was applied.
- This paint could be an oil based or alcohol based stain kill to cover over stains and spills from the previous owner. These types of paints take time to off gas.
According the US EPA website, formaldehyde is a colorless gas with a pungent, suffocating odor at room temperature.
I would start by keeping the doors on the cabinets open for a week if they were painted and, if possible, keep the windows of the apartment open too. This will allow them to air out as the cure.
If this doesn't work it would be in your rights to notify the landlord and request he looks into it.
For more information:
Read "Is there a finish I can use to seal MDF surfaces on a changing table for my baby's nursery?" a Q&A answered by Debbie Sek.