To address your question about antibodies, produced by antigen-specific B cells or plasma cells, I'm first going to address how you activate a B cell.
Naive B cells are produced in the bone marrow with antigen specificity encoded in it's B cell receptor (BCR), a product of VDJ recombination. Each B cell has a specificity toward a single antigen through it's BCR, much like T cells have a single-antigen specificity through their T cell receptor (TCR).
The ways that B cells are activated differ and I think you can get an idea here in 9.1 and 9.2. The take home point is there are T cell dependent and T cell independent pathways, but typically multiple cells are involved.
So to be certain, however, antibodies come at the late stage of infection, they do not start the process. As a matter of first response, you typically have the innate immune cells and the complement system responding. B cells have complement binding proteins that can link innate and adaptive immunity, like CD21.
Also, In the case of allergic reaction, it's different because it requires a priming stage by an initial contact with an allergen, and then the IgE antibodies present on mast cells during the second encounter cause the reaction, but here we'll focus on pathogens.
The entire process of antibody production takes place generally at the B cell receptor locus. The B cell receptor is expressed as two insoluble isotypes in a naive, circulating B cell: IgM and sometimes IgD. Keep in mind that secreted IgM and membrane IgM are structurally different. BCR IgM is monomeric, not pentameric like its secreted counterpart. The significance of IgD is also under investigation, but some research shows it's indispensible for responding to large multi-valent antigen when the B cell is already anergic (ref).
Whether the antibody is membrane-bound or secreted depends on post-translational modification, and these are affected by the activation state of the B cell (I like this reference). So when the B cell activates as it does in the above reference, either T-dependent or T-independent, two things are necessary: The antigen stimulation, and specific cytokines. Take a look at the B cell receptor locus:
You get an immunoglobulin by taking the variable region produced by VDJ recombination and attaching it to a constant region. The Ig locus has multiple constant regions: Cµ, Cy, Cα, Cδ, and Cε. When it wants to produces IgM and IgD, it transcribes a long mRNA V-Cµ-Cδ and then the cell edits the mRNA into V-Cδ or V-Cµ. The mu and delta C regions are spatially separated so that they are co-transcribed but the other C regions are not. Then it translates and modifies the protein to get a secreted or membranous Ig. B cells that secrete antibody are activated and a referred to as plasma cells.
But, if you're being stimulated by interferon-y at the same time, B cells can class switch to IgG by editing the gene locus so that the mRNA produced is V-Cy. If the cell is receiving Th2 cytokines like IL-4, it can make IgE by editing the gene so that the mRNA is V-Cε. The B cell actually deletes the other C regions in the DNA so it never reverts back. I go over class switching here.
Does that make sense? The antibody requires a concerted effort of other cells, and intracellular splicing and protein-modification machinery. See my favorite text, cellular and molecular immunology, 8th ed. for a powerful reference.