What he said is right on point. In my avatar picture I am about 218lbs and I am about 6'3" tall. I have a fast metabolism and to gain weight I need to eat about 5000-6000 calories a day and at that I can get up to about 235. I've gotten above 240 before but I was eating so much that it was uncomfortable and the gas was horrible. I have a full time job so that really isn't an option. On the bright side I can maintain 218lbs at 3600 calories a day. You just started eating this way so it is tough right now but you will get to the point that eating 3600 calories a day is easy. I highly recommend adding in shakes as they are much easier to digest then solid meals. As others have said you may have to watch the milk as it can get to be to hard on the stomach. I often mix my shakes with 1 cup of whole milk and the rest water if the milk is starting to get to me. I will add olive oil to the shakes if I need more calories.
As for the stomach sticking out yes that is from the food. When you stop eating as much your stomach will not stick out so much. You can probably already see the difference from when you wake up and your stomach is empty vs when you go to bed and your stomach is full.
If you get tired of eating this way just taper it off for a little bit. You will feel better and your body will do well from the break. Just make sure you don't eat so little that your stomach shrinks back up all the way.
Sounds like you are doing a good job so far so keep it up.