Interrupt routine for button somehow respondng to room lamp turning off and on
Yours is a problem of EMI (electromagnetic interference). The ballast from the fluorescent light may interfere via two mechanisms:


Conducted EMI through the power lines (unlikely). In order to rule out this condition, power your Uno through a battery or a battery-powered device (a laptop disconnected from mains). If EMI effects disappear, then you have a problem of conducted EMI and you must use some kind of power-line filter. If it doesn't disappear, then it's a problem of radiated EMI (continue reading).
Radiated EMI (most likely). There are some things you can do to mitigate its effects:


Use wires as short as possible.
Twist wire pairs whenever possible.
Avoid operating conditions that leave inputs unterminated (be sure they're always either pulled up or low). This can easily happen when switchs are used and they leave an input in a high-impedance (disconnected) state.
Increase the debouncing time or use a more robust, glitch-tolerant debouncing routine.
Consider polling the input instead of using an interrupt. However, doing this will be of little use if you don't improve your debouncing routine.
Consider adding hardware debouncing.



Regarding the last three points, I recommend you to read this this. You'll have a better grasp about the art of debouncing inputs.

SPOILER: One thing you can do to make your debouncing routine far more robust is to wait for N consecutive readings with the same value (to happen during a given time T = N x Interval) before considering it good, instead of just waiting for a second reading after a constant time T.