You've not said what phone model or what OS version. This is important, because Android 6.0 introduced a new way of using an SD card for app storage, and HTC do include that option. So if you are running 6.0 or later you have the option of "adopting" the SD card as an extension of your internal storage, at the cost of the card being encrypted (so no other device can read it), making it like the internal storage in another way as well. And if you do that, back up the card first, because everything on it will be deleted during the process.
If you are running an earlier OS version then you can only move the apps that allow you to move them. No pre-installed apps can be moved, and not all user-installed apps. Also this only moves a part of the app, and does not move internal app data. But if you've moved all it will allow then that's it, you can't move more. All you can do is delete unused apps, clear their data, etc. And if you've gone below about 500 MB then yes, it won't let you install more apps: Android needs some storage free as working space, so will prevent you from installing apps before you run out of space completely, in order to keep some free space for working storage. And apps install to internal storage, so free space on SD doesn't matter for this purpose.
If you are in the second position there are some more things you can do, but you need to be rooted to do those.
