Using a 220ohm resistor in a mains circuit?
Yes, But...

"Normal" resistors do come in different sizes, voltage ratings, tolerances, and power dissipation ratings.  You need to replace the burnt out one with one which matches.

Resistance: Replace 220Ω with 220Ω. Easy

Tolerance: A resistor which is used in series with a motor is unlikely to have a fine tolerance. To be on the safe side, you should replace with the same or better.  E.g. 5% could be replaced with 5%, 2%, 1% etc.  Look at the last colour band to see what the tolerance is.

Voltage rating: There is no easy way to check the voltage rating of the resistor.  Unless you have a particular reason not to, just choose a voltage rating well above the mains voltage in your country.

Power rating: There's no easy way to check the power rating of the burnt out part either.  Most resistors of a given size have the same power rating though, so if you replace like with like, that should be fine.  Even better, you could go for a larger resistor with a higher power rating, that way it might not burn out again.

Size: Provided you can fit it in, there's probably no harm in picking a larger resistor.  The main change is the power rating.  Be careful about clearances though - the resistor may have lots of space around it to make sure it doesn't arc to another component or to the case.  Don't put a larger resistor in if you can't maintain that spacing.