iPhone SE memory issues...

3.8 GBs is NOT a whole lot of free data storage space left.

iOS devices need a minimum of 3 GBs of free data storage space for iOS to work nominally.

2 GBs is an absolute minimum.

You cannot completely fill up any iDevice to maximum capacity, EVER!

So, it is VERY possible you do not have sufficient enough amount of storage to download any apps.

This is the problem with 16 GBs iDevices and why Apple has, silently, discontinued selling them.

A 16 GBs iDevice, after formatting the flash drive and installation of iOS and default apps, leaves the device with only approx. 13 GBs of free data storage space, plus leaving approx 2.5 to 3.0 GBs of storage space for the operation of iOS, a 16 GBs Apple iDevice is only left with 10 GBs of practical free data stirage space.

It's not a lot of storage space on these devices.

If you need to free up free data storage space on an iPad/iDevice, you need to start by backing up your iPad to either Apple's iCloud or by connecting your iDevice to a computer running the latest iTunes.

Then delete any installed apps that you no longer use or use infrequently enough that they aren't missed (you can always reinstalled any purchased or free apps at some time later, as you need them).

Thin out/delete any music/videos/movies/TV shows/images/eBooks/eMagazine/iBooks/audio books/Documents/PDFs, etc.

Delete any old saved emails that maybe saved to your iPad.

To permanently delete photos/images off of your iDevice go into the Photos app and find the Recently Deleted folder/album and permanently delete any photos/images stored in that folder/album.

Also, you can check to see what stuff is eating up all your valuable data storage space by going into the Settings App,,General Settings Panel, in the right hand column, tap Storage & iCloud usage panel, in the top Storage Panel, tap the Manage Storage panel, wait for a list of apps to generate that will tell you how much space each app is taking up on your iDevice.

Good Luck to You!