Is getting side effects from emergency contraceptive a sign that it worked? Or is it normal to get side effects?

No it's not a sign . Emergency contraception works if it is around the time you expect to ovulate.If you have already ovulated ,example 5 dYs prior.It will not work.There are common side effects we see like delayed or earlier periods.I f there is no period within 2weeks of anticipated cycle.,I woul follow up with a pregnancy test.
Common. Side effects are common. Pretty much anything that has effects also has side effects. Many drugs are used for what were originally thought to be side effects. Thalidomide was marketed as a sedative but found to cause severe fetal anomalies ( flipper babies). It is now being used to treat lepers because of the same side effect that caused the birth defects. .