That is not what interrupts are for!
As a beginner, it is incredibly unlikely that interrupts will be useful to you.
A common "newbie" misunderstanding is that an interrupt is a mechanism for altering the flow of a program - to execute an alternate function. Nothing could be further from the truth! 
An interrupt is a mechanism for performing an action which can be executed in "no time at all" with an urgency that it must be performed immediately or else data - information - will be lost or some harm will occur. It then returns to the main task without disturbing that task in any way though the main task may well check at the appropriate point for a "flag" set by the interrupt.
Now these criteria are in a microprocessor time scale - microseconds. This must not be confused with a human time scale of tens or hundreds of milliseconds or indeed, a couple of seconds. A switch operation is in this latter category and a mechanical operation perhaps several milliseconds; the period of a 6000 RPM shaft rotation is ten milliseconds.
Unless it is a very complex procedure, you would expect the loop() to cycle many times per millisecond. If it does not, there is most likely an error in code planning; while the delay() function is provided for testing purposes, its action goes strictly against effective programming methods. The loop() will be successively testing a number of contingencies as to whether each requires action, only one of which may be whether a particular timing criteria has expired. Unless an action must be executed in the order of microseconds, it will be handled in the loop().
In this case, you need to break up the "rainbow" function into its component parts, and test for your "interrupt" condition regularly during those parts. This has been discussed frequently here, but it is difficult to find the exact discussions. Mike may have a convenient link.
So what sort of actions do require such immediate attention? Well, generally those which result from the computer hardware itself, such as high speed transfer of data in UARTs(, USARTs) or disk controllers.
An alternate use of interrupts, for context switching in RTOSs, is rarely relevant to this category of microprocessors as it is more efficient to write cooperative code as described above.
Referring to your valid point about checking for my interrupts constantly, I've got the loop constantly checking for button changes(which, in my understanding are interrupts in my code(please correct me if i'm wrong!)) which are classed as interrupts as they need to happen in no time at all...