You might have increased your requirement for biotin. Biotin usually helps improve my skin condition and makes it less dry then more that I take. Incidentally, if I have a skin wound, my biotin requirement increases dramatically which can make my skin dryer until I increase my biotin intake. I try to take 2x10mg /day normally but that can increase further if my skin is healing.
Swanson 100x5mg capsules from Healthmonthly is the cheapest place that I know.
You might have a tendency towards skin autoimmunity like I have myself.
I have tried many types of skin lotions and also, substitutes for "soaps" … and I also try to be extreme careful about what goes in a washer or dryer, so as to have all fabrics have fewer irritants to my skin.
I assume that each person finds different stuff to apply, that helps any little bit, or does not, for them individually.
For some time, I used only pure olive oil soap. Then at times, all glycerin bar seemed ok.
Now I use either liquid Shea Butter Body Wash, (unscented) the brand is Alaffia. Or I use Vanicream cleansing bar, sometimes.
For lotion to apply, I often use pure almond oil, by itself.
Or I also like the CeraVe brand. There are 2 moisturizing creams, of theirs, that seem helpful for me.
Just ideas. I have no idea, what might help anyone else.
Lotion with 12% ammonium lactate is the only thing that has worked for me. My skin became very itchy when I became hypothyroid and now that my thyroid hormone levels are better my skin is getting softer.
Here are some brands available in the US. In the UK if you go to a druggist and ask for lotions with 12% ammonium lactate they will know what you mean.
The lotion works best when it is applied to wet skin within 5 minutes after getting out of the shower or bath. Depending on how dry your skin is you may need to use it twice a day. I found that I needed to use more at first and now I'm using less.
It may be a good idea to have your thyroid levels checked. You could ask your doctor if they think there might be other reasons for your dry skin.
I too, have found that it does help if it is possible to apply oil or lotion, while skin is wet,
so after bathing is preferable, but often not possible for myself,
so when I am able to,
I pat skin with a warm, wet washcloth, before applying any type.
Rosehip oil is very soothing and moisturising and very good for dry skin. You need to be aware of the type because it can come in a red colour or yellow/semi clear colours. The lighter colours tend to be more refined whereas the red less refined. The red stuff you won't want to put on to anywhere highly visible.
It can get a bit expensive, it's best to try small samples until you find something that suits. It is recommended for dry and mature skin.
Test to make sure you are not allergic to it. Do not put it all over your face before you test it to make sure it suits your skin.
I dislike commonly available moisturisers which tend to contain nasty chemicals like paraffin etc. Oils put up a barrier which helps prevent the skin from drying out and is more like natural sebum.