The problem is that, even when apps are installed on the SD card, they have a footprint in regular memory. Sounds like yours is full.
You need to uninstall some apps you're no longer using or maybe uninstall updates for apps that you don't use but can't remove. Alternatively, root the phone and remove all the bloatware - that would usually free up a decent chunk of space.
In the end though, if you keep installing new apps without removing old ones, you are going to run out of space.