Learn English – Which one is correct? “On a TV show” or “In a TV show”

They are not interchangeable. I almost never use or hear other people use the word 'program' to refer to a TV show. This might be a regional thing. (I live in the Midwest of the US.)

A TV show can refer to something like the news. However, you would not use "show" to refer to a special, or something that doesn't come on TV regularly.

A TV series would be any show that has seasons. (which in British-English are called 'series') A news show or late night show doesn't have seasons in the same way that a comedy show or something like American Idol does.

Concerning prevalence of use, you made a little mistake in Ngram: You looked for "in my journey, on my journeys". Using only the singular, we see a quite different usage curve.

More to the core of the question:

The noun 'journey' is also used metaphorically. "In my journey to become a better programmer, many people helped me."

Here, 'on' is slightly off.

On the other hand, if 'journey' refers to an actual, physical journey, at least in the singular 'on' will be the better choice, as it (loosely) describes an event, even if that event may stretch over a longer period of time.