My heart goes out to you. It is already challenging to be a first time mom, trying to figure things out, but to go through this...that's tough.
I am mom to 4 awesome children, all of whom I nursed. My second baby sounded a lot like your little one. I nursed him as well, and he cried almost non-stop, otherwise. It was overwhelming. But here is what we did. Take out not only dairy, but eggs, OJ, and tomatoes too. Those are pretty big culprits in making babies fussy (besides the well-known broccoli, cabbage, and beans).If the fussiness disappears, you know you have found the culprit! Just add the items back in one at a time, every six days or so. When the fussiness returns, the food item you most recently added is the problem. That is how I found my sons' allergy. He was bleeding in his diapers, and I used this method to narrow the allergen down to dairy. Turns out my little one also has a dairy allergy. It is quite common in infants.
Something else to think about. You said you are nursing. I realized in hindsight that the other part of my sons crying was a problem with me. I was hyperlactating (making too much breast milk), which causes the baby to get too much sugary "skim" milk and consequently makes them gassy and very fussy. Also, the "skim" milk won't fill them up, so they are hungry a lot, and want to nurse all the time. My son nursed at least every two hours, 24 hours a day. I discovered that now because it happened to my 16 week old. The first sign was that she had green diapers (well past the newborn green diaper stage), which should be yellow for a nursed baby. Then she started getting really fussy. It was also indicated by her body language: chugging the milk while crying because it was coming too fast, seeming to fight with my breast...lots of kicking and angry squirming of the body, and of course intermittent crying at the breast. The way to solve it is to drink some mint tea (it slows milk production down)and to nurse from one breast at least 3 times in a row before switching to the other. The result is less milk to chug, and consumption of the skim milk so they get to the good stuff - the hind milk, which is creamy and has plenty of caloriesso they stay full and happy. The result for the other breast? Since it is not being emptied as often, its production of skim will slow down, and you won't make as much! But you must keep up that pattern in order for it to work. It takes a couple hours to a couple days. (Nurse three times on right side, ignoring the left. Then nurse three times on left side, ignoring the right breast…this is called block feeding.) If your milk has slowed down since you have given him some formula, don't worry just start up with the pattern. Your breasts will follow your lead and meet the baby's demands. Also, during your block feedings, if your “ignored” breast becomes too uncomfortable, the baby may nurse on that side, just to relieve the discomfort. But not too much, so you do not stimulate the production of skim.
My little one also has reflux. The body language was similar. Scrunching up legs, fighting the breast, crying, and strange throat noises I had to imitate for the doctor:). Pediatirician put her on Prevacid and that made her belly aches worse (it increased her "leg scrunching" and crying). So we switched her to Pepcid and she is doing wonderfully! Pain is gone! She still spits up A LOT, but thats fine with me as long as she is not in pain.
I hope this helps. Try not to stress out, the baby will follow your lead. Sounds like you are doing a great job of being observant and investigating what’s going on. Follow your gut...mom's have a good sense about their babies. I have included a website that might be helpful to you if you think hyperlactation is the problem.
http://breastfeeding.hypermart.net/toomuchmilk.html
Best of luck to you! I will be thinking of you!