Sorry that you are going through this, must be really hard.
Hudson is only 16 months, doesn't throw any tantrums YET, but I can definitely see a difference. When he was on regular formula for the first 10-11 months he was always cranky, always whiny, clingy. I attribute this to the allergy symptoms. I mean the formula was causing tummy upset, making him have bad eczema that obviously was really itchy, constant scratching himself, plus he was always congested. Just imagine feeling like that every day all day I'm sure it would make you a monster, well that's how I viewed it.
I don't know if the behaviour change is a symptom of the allergy or a reaction to the symptoms, if you know what I mean. Because he felt like utter carp it showed it in his behaviour.
I'm am starting to feel the same way as you about my son, though not as severe. He's been on cow's milk for 1 week, now it's half milk and half Neocate. Today he was SOOOO whiny, and clingy, and throwing things and anything seems to set him off to make him "mad" or upset enough that he'll push his sister out of the way, and purposely go over and throw her toys she is playing with or the remote on my lap. I think that maybe he's starting to feel icky again and thus being cranky and I think I'm seeing a behaviour change.
But I'm not 100 percent sure that is what it is or if he's just in a bad mood.