Yes, but as of now we only know of one virus, the rotavirus, that produces toxins. In rotavirus it produces NSP4, which is an enterotoxin or an exotoxin that targets the intestines specifically. What is more commonly seen is lysogenic conversion or the changing of a bacterial phenotype due to a phage inserting its genome into a bacteria. An example of this is Diptheria which, doesn't produce the diptheria toxin without phage infection, but with it does. This occurs because the gene for the toxin is carried on the bacteria phage and is inserted into the bacterial genome and then expressed by the bacteria.
As for your question about viruses and allergies, viruses aren't seen as causing an allergic reaction because the immune system mechanism is different. In allergies, antigens, molecules that our immune system recognizes as foreign, stimulate an IgE mediated immune response which causes mast cells to degranulate and release histamine which causes all of the typical allergy symptoms. In a viral infection our cells get infected and a cytotoxic (CD8) T cells response is initiated, these cells go around killing infected cells by inducing apoptosis, also know as programmed cell death, in them. Here it isn't termed an allergy because it is adaptive to kill infected cells in order to eliminate the virus, whereas in allergies a bit of pine pollen or peanut antigen wasn't going to harm our system and the response is detrimental rather than helpful.