I went without dairy for 18 months, it was horrible at first but I got used to it, and to have a calm, non-colic-ridden baby that wasn't doing explosive green slimy poos and screaming from silent reflux when put down made it worth it.
But farts alone are not enough to suggest a dairy intolerance, babies with cows milk protein intolerance (and it's the protein, not lactose they are reacting to) also tend to have reflux, eczema, acute colic, explosive green slimy poo, and or blood in the poo/slime.
Wind is nasty, but can be eased by tummy rubbing, leg cycling and regular burping. I wouldn't stress about dairy etc unless it's really nasty and has other symptoms.
Nothing wrong with a glass of wine, tis a myth you can't drink when bf.