Not sure about organic for these, but in keeping with the main thread, I'm another fan of Neutrogena Swiss Formula for day use
https://www.walmart.com/ip/Neu... (you can touch the refrigerator, microwave and such without making a greasy mess everywhere). Had to give BagBalm away - couldn't stand the smell. It is predominantly petroleum jelly and lanolin. I prefer Aquaphor (you can find it in the baby aisle)
https://www.walmart.com/ip/Aqu.... Similar ingredients without that smell. It is mostly like a Vaseline - I tap each fingertip and thumb - then tap cuticles of my other hand and work it around the cuticles (not the whole hand for this as it is greasy). Allergic to both Polysporin and Neosporin - it's my wound care as well - with dry skin it really helps to keep any scratch or cut moisturized and sealed. I've done the cuticle thing with Vaseline as well.
For non-allergic lotions (skin sensitivity, again don't know about Celiac), Aveeno and Cetaphil are the best. Others may say hypo-allergic but not really be so. Aveeno skin relief in a tub is great for night time rejuvenation
https://www.walmart.com/ip/Ave... (their bottle / pump lotions are the same as everyone else as far as hand care). But these are my 2 go to for non-allergic sun screens.