Guess I was under-estimating my protein intake then.
I'm looking at your diet again, with whole milk a gallon a day would be about 2300 calories and about 130 g of protein. You say you are getting only a little more than bw in protein, so I will assume below 160 g of protein. If you are eating between 3500 and 4500 calories a day, I don't know how you aren't getting more protein. Do most of your meals mainly consist of carbs and fats? any vegetables? What other foods are you eating (you may be underestimating your intake)?
If you don't want to buy protein powder to replace some of the milk, other possible foods you could buy are Fage Greek Yoghurt (23 g of protein per cup), Kashi Go lean Cereal (13 g per cup), Barilla Plus Pasta, and of course tuna and chicken breasts (I don't pay attention to the price of these products, so I don't know if they fit in your budget).
About the water intake, milk is about 85-90% water, so you're probably getting enough water. 6 hours of sleep may be a little low though.
Based on the lift stats you gave, I am assuming you are following the beginner routine in the OP. You can always try to add some more lifts - pullups and parallel bar dips for instance. And again, you need to be patient - as long as you are gaining some weight and increasing your lifts consistently.
I have 3 eggs, greek yogurt, buttered toast for breakfast
lunch I just eat whatever leftovers I can find in the refrigerator. This week it was mostly homemade mac and cheese. (Lot of cheese, carbs from the breadcrumbs, and the pasta)
For dinner I eat whatever is made. My dad makes good stuff. Usually pasta and meat dishes.
And then the GOMAD.
I have protein that I use for workouts and whenever else I feel it. Peanut butter sandwich before bed sometimes. I don't track anything since it would be too hard to track since I usually don't prepare the food.
I can think of another problem. Wednesdays and Fridays I eat shitty sometimes. I go right from school to work (and the work is fairly strenuous) Weekends are also a slight problem since I work 10-12 hour shifts and only get 1 half hour break to eat,