No, relying on your own personal experience to make determinations does not make one a "conspiracy nut".
It does when you are saying everyone else, including those who have spent quite a lot of time and effort either determining or using this information going directly against your "determination", which then also requires you to ignore loads of evidence which clearly shows you are wrong, such as photos from space, which are not all composites, with some at least being alleged as single images (or multiple single colour images combined into a single multicolour image in a similar manner to what a digital camera will do).
The only way you could argue that it doesn't make you a conspiracy nut is if you were isolated from the rest of the world and didn't have access to that knowledge.
But I'm pretty sure everyone on this board knows about photos from space, which clearly show Earth as a round object, like a ball; to someone not critically analysing the photos, they would assume Earth is a perfect sphere, as it appears round from every direction and the difference from a sphere is not noticeable by the naked eye. While a critical analysis with actually measuring the size shows it is more an oblate spheroid, and the uncertainty due to the size of a pixel allows it to not be perfect.
And likewise, I'm pretty sure everyone on this board knows about GPS, which is based upon satellites orbiting a round Earth, and using math based upon a RE to determine your position.
And likewise, I'm pretty sure everyone on this boards knows about the various claims of objects in space, like the ISS with people on it and the trip to the moon and probes sent to other planets.
So if you are aware of that and still claim Earth is flat, you are appealing to a massive conspiracy.
The only way out is to claim extreme wilful ignorance, where you are choosing to be ignorant of all the evidence available which shows Earth is round.
Otherwise, accepting the existence of all that evidence to avoid claims of a conspiracy or wilful ignorance, the best you can do is say you don't know the shape of Earth.