I think you've got your definitions mixed up. Feeling IS a rational process, rational meaning based on reason and making choices. I know the NTs are called "the rationals", but that's based on an incorrect using of the term. Feeling is not "logical" though, which is a particular kind of reason, which might use something like an "if... then" statement. Basically, Thinking is based on logic, systems, and is impersonal criteria, whereas Feeling is personal and based on values and empathy. Both use reason.
When you say "I find it useless to resist typing since it's descriptive" I think you might be using an Fi principle to guide your reasoning, because that statement isn't clear to me regarding why the conclusion follows from the premise.
To describe what Fe is like, one major aspect is that the things I do are often tailored to fit an audience - they are done with another person in mind, or the general group, which can give me a "teacher" or "helper" persona. This seems to mirror what you said about making choices based on authenticity as a description of Fi. Authenticity isn't the only aspect of Fi, but it's definitely related.
So I guess the difference between Thinking and Feeling is whether your reason is guided by the rules of a system, or the nature of living beings (seen from the perspective of consciousness, as opposed to also seeing the lifeform as a system in itself). That's why Feeling is tied to empathy - it's more psychological in nature, often referring to a person, with that person being your internal guidance system in the case of Fi. Ti also uses an internal guidance system, but Ti is very detached, whereas Fi is more heartfelt. Functions that play the same role, like Fi and Ti, have very similar natures in terms of what they do, but they use opposing criteria which can kind of "undo" each other. With Ni and Si, Si focuses on the known and tries to become more and more certain, whereas Ni focuses on the unknown and tries to dig deeper and deeper, but both are about the subjective way in which information appears in the psyche, being on the one hand a point of view, and the other hand a way of channeling information from the psyche (concepts for Ni, memories for Si). Ti has a tendency to divide things, noting the distinctions which define one thing as separate from another, whereas Fi has a tendency to unite things, often trying to find a compromise where things can be both ways.
So yeah, Feeling and Thinking are both rational, they just reason things out differently. Your usage of the terms rationality and logic strike me as incorrect, so when you say that your emotions follow logic, I don't know if you're talking about the interplay of Thinking with Feeling, or merely noting the simultaneously emotional and rational nature of the Feeling function.