You can take prescribed medication to HMS Raleigh as long as you take the prescription with you and the information has been submitted to Capita / SEMC. That way the medical team at Raleigh know and they will be able to re-assess / examine and continue the treatment if necessary. Due to constant hand washing and use of anti bacterial gel during the pandemic there is a lot of dry skin out there.
If you have any doubts inform your AFCO, let them know what you are on and how long you have been using it and they can contact the Service Entry Medical Cell (SEMC) in Portsmouth and they will give you a Medical answer. If there is a problem they will let you know. If it is not a problem then it will put your mind at ease.
It is best you await the response from your AFCO. Any response on here will be anecdotal and have little relevance to your own situation.
Eczema has been discussed in years gone by on this forum and I don't think the rules have changed much so it may be worth a search in the box in the top right hand corner to see what was said.