I mean ,In primary response IgM is produced (IgD as well) ,In secondary response various types of antibodies are produced . So how do I detect which antibody is B cell is producing at a time.
The major antibody in the second exposure is IgG and in the first exposure it is IgM. IgG and IgM would be produced by Plasma Cells, which are effector B-Cells activated by Cytokines.
If you want to see which antibodies (not just antibody types) are produced by the B-Cell, I would suggest transforming a GFP gene into a Naive B cell and using a Restriction Endonuclease and DNA Ligase to insert the GFP gene to the 5'-end of the Constant (C) region of the Antibody producing gene. Then, you could see which Antibodies are produced by B-cells since the Antibodies would fluoresce.
Note: I am currently in high school so I don't have much experience with Immunology, so there might be a few things wrong about my answer. However, I tried my best to answer the question. Hope this helps!!