I have this exact same problem. I react to absolutely everything. I was going out my mind trying to find something that didn't leave my face red and itchy and the only line I can use is a brand called Pai. It's quite pricey but worth every penny in my opinion. I'd rather spend £34 on something than have damaged, irritated skin. I use the Geranium and Thistle moisturiser but they do a few different ones.
They do samples too for not much. x
Firstly, you have a beautiful face regardless of your acne.
dairy could be a factor because it contains a huge amount of hormones which then get pumped around our already hormonal body, so it's just hormones piled on top of hormones. + cow hormones are strong because obviously it's needed to make baby cows grow up big and fast. So do try cutting it out or reduce it. Almond milk is always an alternative. Or soya, which tastes a lot nicer than almond, but I've read that it can trigger acne in some people too. although a lot less than cows milk.
Also, the moisturiser you're using. It might be oil free, but if it's the Neutrogena Visibly Clear one, then there's a whole host of ingredients in there that are even worse than slapping a load of oil on your face. For example, Propylene Glycol is the 2nd ingredient on the list and that's worrying because that ingredient is used in car anti-freeze ! As well as Sodium Hydroxide which can cause a chemical burn after repeated use.
I'm in the UK (I don't know if you are too) but the ones I like are:
This is my fave company ... http://www.handmadenaturals.co.uk/shop/shop.php?c1=FACE%20CARE&c2=CLEANSERS%20AND%20TONERS
Their rose cleanser is the BEST.
I don't use their moisturisers because I'm using something else. but I think they'd be good for you.
http://www.100percentpure.co.uk/Default.asp is also good. expensive though. There's a healing balm on there that my mom used when she had bad sun burn and it totally cleared it up within 2 days. I can't use it though because I'm allergic to lavender oil.
I think something natural or organic would help you. Especially something with rose in because it's very calming for redness. I'm really against using synthetic chemical skincare, especially moisturisers because those are the ones that sink in and really get into our skin and tissue, so any harmful chemical like Benzoyl Alcohol , all the parabens and Disodium EDTA (I'm just listing a few of the ingredients that are in one of the moisturisers you mentioned), they all get absorbed really deep into the skin and damage it from the inside (believe me when I say I've learnt my lesson using chemical products as I'm now stuck with severe facial eczema AND rosacea, which have been caused by them)
Try something natural, organic isn't a must, it just means the quality won't be quite as good.
I've read so much about people using green tea to calm redness/red zits . You're meant to make a cup of green tea as you would normally and pour it into a spray bottle, spray on skin after cleansing and then moisturise. I've heard wonders about it and I'm gonna try it myself later !