I whistle a lot, and I'm fairly decent at it. Recently I was walking up the stairs in a house while whistling. As I whistled, I found it difficult to hit a specific note in the song that I would normally be able to whistle. I found this strange, so I stopped in that exact spot on the stairs, and tried whistling that note. It felt as though there was some kind of resistance when I whistled that exerted pressure on the pitch either up or down to a different note at which there was no resistance. It seemed really weird to me, but I stood there for a few minutes testing different pitches, and it really seemed as though there was a certain pitch that didn't resonate well in that space, and not only that, but I felt some kind of pressure on the note that I was whistling to move to a different note. Is this kind of like the opposite of resonance? Or am I crazy?
This sounds like destructive interference interacting with your attempt at driving a resonance.
Normally when whistling or singing in the shower or a stairwell, certain pitches get nicely amplified by resonance. These room modes are standing waves where the pitch fits into an integer number of wavelengths between reflecting walls. The sound source corresponds to a pressure amplitude maximum, but if it is a quarter wavelength from the wall the reflected pressure wave will exactly cancel it. So at least in some places for each pitch there should be "dead" spots.
(An interesting question is why we rarely observe them, while shower singing easily finds resonances where our voices fill out well. It might just be that we unconsciously modulate the pitch to where it resonates rather than keeping the same pitch and moving.)
It could be possible that the produced sound echoes in the room and the echo makes destructive interference with the original sound. It would affect different harmonics differently however, so I recommend also trying to use a the same note an octave higher or lower to exclude this possibility.
Usually, the stair well in a house has fairly hard reflective wall surfaces and nothing much that would absorb sound energy. Therefore, there would be frequencies at which a strong standing wave pattern would be produced in the space.
If you were at a position where the amplitude of the standing wave was zero (called a "node") then you would experience more "resistance" if you tried to produce a note at that frequency. You can think of this in simple terms as the sound waves reflecting back from the walls and "cancelling out" your attempt to move the air when you try to produce a note, though of course in a complicated 3-dimensional shaped space like a stair well that is an over-simplified explanation.
This effect is very important in the design of musical instruments, where the sound waves are inside of tube of some fairly simple shape, rather than in an open space like the stair well. It is the basic reason why wind instruments "play" a single note when you blow them, instead of a continuous range of frequencies, and why by changing the geometry of the tube (by opening and covering finger holes etc) you can change the note that the instrument plays.