Facts are based on observations, and observations incorporate, to some degree, our feelings about them — and that’s the basis of your argument of feelings being facts, right?
No they’re not. We observe with our senses. Facts are codifications based on complex cognition and abstract modeling of our observations.
I won’t argue with the Sapir-Whorf hypothesis which seems somewhat applicable to what you are saying. In general, I agree. However we differentiate terms specifically because of perceived relevance based on scientific principles and to increase shared understanding. There are a vast number of shared perceptual frameworks and as individuals, we can incorporate a number of them into our personal framework.
Scientific methodologies carry a lot of relevance because they incorporate self testing and, more societies that have otherwise very different shared perceptual frameworks can agree upon it as a framework that can, at least some degree, co-exist with their other frameworks.
We differentiate between facts and feelings because that differentiation is relevant enough for us to discuss them as separate from each other.