The main problem is that moisturisers are not all made equal; choosing one that contains an emollient is good, and avoiding fragrance may be necessary if you have sensitive skin. I’m not sure which ingredients cause your skin to feel dry, but if you know and avoid them, also good!
To be sure of getting the most out of a moisturisers, you need to know what your skin actually needs, and it seem that you do. Dry skin and atopic dermatitis can result from both endogenous and exogenous causes, but whichever it is, the appearance, function, and feel will be similar and can be effectively improved by choosing moisturiser ingredients with care - so look at the back, ingredents’ list and you can pretty much ignore the marketing!
To improve very dry skin and/or that with atopic dermatitis you will benefit from using the following four types of ingredients: occlusives, emollients, humectants and skin barrier modifiers. And there are several possible candidates for each of these four groups, some will suit you better than others and some will be more effective, you may have to try a few. I would recommend listing these and then looking out for them in a moisturiser:
Occlusives
The most effective of the occlusives is petrolatum, but it doesn’t have the feel most people prefer. You can choose castor oil, fruit oils or for a less oily feel, silicones - commonly dimethicone, or a silicone-like effect, from Isoamyl Laurate (Gosulin) from sustainably grown palms. It matters how much is in a product, but most products containing these will use a reasonable amount.
Emollients
Commonly used, good emollients are: cetyl stearate, colloidal oats(this should help reduce itching and inflammation too), coconut oil, and a couple of the occlusive ingredients, like the silicones and castor oil are also emollient.
Humectants
Glycerine is a very common and excellent humectant (a bit sticky over 4% though), hyaluronic acid, propylene glycol and sodium PCA are all good and commonly found - in fact if sodium PCA is in a moisturiser with glycerine, it will make the latter less sticky.
Barrier Function
The ingredients I would look for, to improve barrier function, in the given situation are: ceramides, which are naturally part of intercellular lipids in the skin and often depleted in very dry skin; urea (one of my favourites, it’s been around for years, is reliable and effective at increasing the water-binding sites on depleted skin cells); lactic acid which stops the skin cells clumping together excessively, niacinamide, (another I have used for years), it reduced trans epidermal water loss (TEWL) and helps repair a damaged skin barrier, and panthenol (vitamin B5) which seems to strengthen the skin barrier over time. Chamomile and calendula extracts or hydrosols have proved useful for this condition, so look out for them on the ingredients’ list (Matricaria recutita flower and Calendula officinalis flower).
There are many to choose from, so I have named the ones that should be fairly easy to find and have good evidence to support their use. If you want the product to feel comfortable, I wouldn’t use something with too much petrolatum as it can feel gloopy (it does massively decrease TEWL, by around 99%, but you skin will probably feel sticky). I don’t use it, as I tend to stick to naturally sourced and sustainably farmed ingredients, but that still leaves a number to choose from.
Colloidal oats, chamomile and calendula will all be soothing. Urea, niacinamide and panthenol B5 are gentle and effective; a fruit oil, shea or coconut butter with either hyaluronic acid, glycerine, and/or sodium PCA and you’ll have found a very nice moisturiser that should make your skin feel much more comfortable.