"Nothing" doesn't exist. We use the term to describe the concept of the absence of something.
What is "cold"? It's the absence of heat. "cold" doesn't actually exist. We can't measure it. Instead, we measure heat.
What is darkness? It's the absence of light. We can't measure darkness because it doesn't exist, but we can measure light because it does exist.
When you cut my hair and I feel nothing, I'm merely using that phrase to mean I don't feel pain or a particular sensation. It's the absence of feeling.
For example, if i take a water bottle and determine that it should be completely full, but it isn't, i can then claim that the bottle is Nothing, and not a bottle.
You can certainly claim that, but it wouldn't be true. The bottle exists, but there's "nothing" in it. The fact that there's "nothing" in the bottle doesn't stop the bottle from existing. It doesn't turn the bottle into "nothing".
Your thinking was reasonable until you got to the last paragraph and starting applying "nothing" to things that are empty, then it turned fallacious. The container is different from the thing that it can contain. They are separate entities. An object being empty doesn't result in the object being "nothing" - it's still a thing but merely "empty".
If I hold a red soccer ball, that doesn't make me a red soccer ball, does it? In the same way if a bottle has "nothing" in it, it doesn't make the water bottle "nothing".
The container doesn't become the thing contained. That's the principle that will fix the problem for you.