It's worth a try, mrsFlorrick. For me the maize certainly seems to be the cause (or a cause anyway). Going by my little "experiment" over Christmas, eating gluten free Christmas cake and chrismas pudding (wheat free/gluten free but both containing maize/corn derivatives)... 3 days, slightly blotchy skin the first day and painful patches of pustules on both cheeks, read nose and raised blotches on forehead, along with broken veins round both nostrils!!! Sounds dramatic but actually very mild/minor I'm just obsessing over my own stupidity. I probably just look rosy cheeked to other people. My eyes/kids are quite red too. Still good motivation to get back to clean eating now.
I was low carb for many years (5?) and my skin/other issues were better (and I lost a lot of weight), but it was going fully grain free that did the trick - redness and rashes settled quickly but the little veins took longer, they gradually faded and one day I realised I didn't have any.
But - if you have a sensitivity to maize/corn, you have to be a real label hawk, or make everything yourself from scratch, it's in bloody everything! Corn, cornflour and modified starch are the easy ones, but there are dozens of derivatives such as dextrose, hfcs, glucose-fructose syrup, Xanthan gum...
In a lot of ways it's just easier to follow paleo or primal because all the recipes are completely grain free. I started off dairy free too, but now have cream and butter (and small amounts of raw cheese). No milk though.
Hth, good luck!