It sounds like you may be having the same problem I was having. After the 10.3 update, both eShop and system updates would just error for me. It seemed like it happened randomly and I thought future system updates might fix it but no such luck.
Can you try this tool and see if it allows you to access the eShop (just install the CIA, run it and apply the patches then open eShop)?
https://gbatemp.net/threads/release-free-multi-patcher.391945/
It worked back for me when I was having issues. In the end what I had to do to fix it permanently was create a new emuNAND, updated it and eShop was working fine. Then I copied all the user data, save data etc. from my old NAND using GodMode9 and eShop was still working. I haven't had any issues since.