Ack!!  Mineral oil is a PETROLEUM product!!  I would be surprised if you _didn't_ react to it, as sensitive as you seem to be!

Here are a few things I use or have used that you might look at.  I've gotten all of these at Sephora.  If you don't have a Sephora near you, you can order online.  If you look at these items online, for the most part Sephora lists all of the ingredients on their website.  There are also lots of reviews, so you can often tell right away that the product isn't for the super-sensitive.  The nice thing with Sephora is, if you don't like it or react to it, you can return it, no questions asked.  It really is that easy.

Josie Maran Argan Oil: Get a small bottle to try it ($15), and a little goes a long way.  It has basically no smell and doesn't feel sticky or greasy.  Really nice stuff, and only one ingredient.  It does make my face a bit shiny, but if it's that or nothing, I'd use it.  http://www.sephora.com/argan-oil-P218700?skuId=1121797

REN Frankincense Revitalising Night Cream:  This is the one that I have used, and you might have an issue with it because it really does have a scent of frankincense.  However, you should look at (and read reviews for) some of the other REN products.  They tend to have the least number of nasty ingredients of any products I've found.  They are, unfortunately, rather pricey, but they work. http://www.sephora.com/moisturizer-skincare#!categoryName=moisturizer-skincare&p...

FAB (First Aid Beauty) Ultra Repair Face Moisturizer and Ultra Repair Cream.  I've found these to be very benign even though they contain dimethicone, which is supposed to be bad and prevent skin from breathing.  The Face Moisturizer is rather light, but the Ultra Repair Cream (particularly the formulation in the small tube which is $12) is quite thick and creamy. It does have a slight scent from the eucalyptus, which the face stuff doesn't have.
http://www.sephora.com/moisturizer-skincare#!categoryName=moisturizer-skincare&p...

Hope you find something that works and don't have to keep putting yourself through all of the trial and error!

Oh, and I have no problem with oatmeal...eat it every morning.   However, I'm eating instant oatmeal, not the real stuff.  I find that for some things, like rice, bread, etc., the less "whole grain" and more processed it is (like boil-in-bag rice), the less I react to it.  If you are eating instant oatmeal, did you make sure there's nothing else in it that you're reacting to?  For instance, does it have cinnamon in it?  Cinnamon is a "warm spice" and thus on the high histamine side of things.

I can't tell you whether you would be reacting to mineral oil, or not (as there are typically other ingredients in the mineral oil, like vitamin E), but, with that said, you shouldn't be "afraid" of mineral oil because it is derived from petroleum (or coal, ergo "mineral oil").  After all, petrol and coal were/are "natural" products.  They were once algae and conifer forests, dinosaurs, etc..  (Kind of funny to be rubbing dinosaur grease on your face to make it look more youthful, but that's a side issue.    Mineral oil is a actually a very "pure", and typically benign substance, from the paraffin side of petroleum, if I am not mistaken.   Nathala being the other side (think moth balls).   So, petroleum derived paraffin and mineral oil are usually OK.   But other things, like moth balls, are not.  

I don't typically react to small amounts of mineral oil on my hands.  But then again, I'm not slathering it on my face everyday.   There is a deodorized Coconut Oil from Omega Nutrition that is healthy for eating and slathering that I do well with in both regards.   I do NOT do well with non-deodorized coconut oil !

Hope that helps some,
Todd in Tenn.