Thanks for writing to us.
You do suffer from anxiety disorder as you rightly pointed out. These happened around 8 hours ago. If something was actually stuck in your throat you will have that feeling that something is stuck, each time you try to eat or drink water or any other fluids. You're probably just anxious and scared since you broke a glass just before having coffee.
Moreover if you ingest a piece of glass, since it has sharp edges its going to get caught in your mucosa and you will have bleeding. You will have blood coming out with your saliva. You will have extreme difficulty in swallowing anything and it will be very painful.
I believe you don't have those symptoms. Sometimes when we are too anxious about something happening, we tend to assume that some symptoms actually exist, when they don't. So don't worry about it. Since there's no bleeding and you have been able to swallow, i don't see any reason for you to be worried.
In spite of all this, if you're still worried then you can go for an endoscopy just to reassure yourself more than anything.
Do write to us for further queries,
Doctor Spring