Is my baby gassy because I am drinking too much milk?

Yes. It is possible. Try reducing your milk intake but make sure you get enough calcium and vitamin d. Give it a week or so and see if it helps.
No. There are many foods that are traditionally considered "gassy" during breastfeeding but milk and dairy are not often included in that list. A good way to see what may be having an affect on your baby is to make a food and gas diary and see which day and times your baby is gassy. Foods consumed in the hours before a feed are the most likely culprits.