I assume you're talking about something traveling through your BM, right?
Wine can carry bacteria. In fact, anything fermented (wine, beer, saurkraut, etc) can carry bacteria. Most mass produced wines like Sutter Home would not contain much because of their high end equipment and quality control procedures, but it's possible that a wine will get oxidized due to too much air during manufacturing. There are several bacteria that can occur during fermentation, but I would be surprised if bacteria would affect BM (don't know for sure about that though). This is where sulfites come in. Any large producer, like Sutter Home, would likely be adding sulfites (or possibly a couple other chemicals in) to kill off bacteria and preserve the wine.
I'm married to a former wine maker and have done quite a bit of home brewing, and I honestly cannot think of any reason how or why there would be eggs or milk in wine. It's possible that those warnings are on there as a cross-contamination concern, but I don't think the ingredients themselves would be in the wine.
And last possible factor could be sugar or honey. Sweeter wines like a rose are often back-sweetened with sugar or honey. Wine producers ferment all the sugar from the fruit, and then add sugar to sweeten the flavor. That allows them to them to reproduce the same tasting wine each time. There's really not much to wine...grapes or grape juice, yeast, sulfites, and sugar (maybe).
I don't know if any of these are the culprit for you, but figured if I laid out what I know it might trigger something for you? Good luck! Hope you enjoy some wine again soon!
