The apriority/experience distinction is not the most well-framed thing in the philosophical world. Your example seems like it could be characterized as introspective, but:
On a narrow account, “experience” refers to sense experience, that is, to experiences that come from the use of our five senses: sight, touch, hearing, smell, and taste. However, this narrow account implies that justification based on introspection, proprioception (our kinesthetic sense of the position and movements of our body), memory, and testimony are kinds of a priori justification. And if we had different senses, like those of bats (echolocation) and duck-billed platypuses (electrolocation), experiences based on those senses would provide a priori, not empirical, justification on this account which takes a priori justification to be independent of experiences based on the senses we have.
Given these considerations, perhaps “experience” should be taken to mean “sense experience of any sort, introspection, proprioception, memory, and testimony”. This sounds like a hodgepodge of various sources of justification but perhaps what unites them is that, leaving aside memory and testimony, these sources provide us with information either about the physical world or our inner world, either the outer world through perception or the inner world of what we are feeling or thinking, or information about our bodies, through introspection and proprioception. [emphasis added]
But so unless there is something useful about distinguishing pure apriority from introspection, one wonders why knowledge of our own bodily states isn't a priori. The above-quoted article goes on to mention that independence-from-experience is often qualified so as to allow that some of the concepts and proof structures we use a priori to nevertheless be read off experience to a substantial extent. So why make the distinction at all, rather than just differentiate kinds of experiences?
But not all is lost: some philosophers do have a non-superficial sense(!) of apriority. Kant asserts that we have passive, active, and interactive states of consciousness, and experience-by-itself (or sensation, anyway) is passive whereas pure understanding and reason are strongly proactive. So even if we discarded the words "a priori" and "a posteriori," we would still have the apparently real difference between passive and active consciousness in play.& Typically, we have some internal control over our own breathing, which control can be used to facilitate mystical or emotional meditation; and meditation itself can go on to supplement contemplation of arcane geometries with a hint of apriority to their base character (the origin of the shapes used in religious architecture and other symbolism).
What of knowledge-of-breathing as analytical? Per Kripke, it is often thought that "analytical a posteriori" is a genuine kind of knowledge, and the stock example of water being H20 is held to be a necessary truth. As a conditional, it might be, "If anything is water, that thing is H20." So would, "If I'm alive, I'm breathing," be comparably analytical and yet a posteriori? (Note that we assume that existing and living are more or less the same in this context.) Actually, if the flow of oxygen is as essential to human life as having oxygen particles is essential to something's being water, then it does seem as if knowledge-of-breathing might be characterized as analytical yet a posteriori.
&Since there are action-based theories of perception, equating apriority with activity and sensation with passivity could be a non-starter, however, unless the role of action in perception (supposing such a role) goes more towards establishing perception as an interactive combination of a priori concepts and a posteriori sensations. For some generally related issues, see also the SEP articles on:
- Bodily awareness.
- Embodied cognition.
- Action and the logic thereof.
- Practical reason and the structure of action.
Or so one might even style knowledge-of-breathing as (potentially) occupying a vague zone between strict apriority and strict experience.