You shouldn't have needed to remove Octoshop Lite before installing the full version, although it's a bit late now...
php artisan plugin:refresh Feegleweb.Octoshop from a terminal to roll back any migrations, although this could prove difficult since you have manually altered the database yourself.
As a general rule, you should never need to manually edit the database schema in any way (unless you're on a not-so-good shared host that prevents you accessing SSH, in which case I'd start looking for a better host).
Because you have already modified the database, you need to make sure the migrations table is correct. It's probably still got references to old migrations, so when you try to remove/install a plugin, it won't be able to find them and thus things break.
If you still have no joy, check your error logs for any clues as to what is actually causing issues.