OLEDs have quite harsh flicker, even those which supposedly don't. They are an emissive display, so every frame the following happens: Pixel shows colour -> pixel forgets current colour and goes black -> pixel is updated with colour for next frame and shows colour again. So your 120hz OLED tv will have 120hz flicker.
LCDs have a subtle flicker, even those with supposedly don't. LCDs use something called inversion. liquid crystals will degrade if kept in the same state, so every frame the electrical current in them is reversed. it creates a much more subtle flicker than OLEDs, but it can still cause problems.
Moving forward, I don't think you'll find an OLED tv that is ok for you. 60hz might be different, but I would expect any 120hz OLED tv to be an issue. Trial and error might find you a useable LCD tv though, as LCD inversion will differ between panel types and implementations.