t3rm3y

hello, forgive me as i dont know the terms, i have a bike i have been riding during lock down, and today the chain fell off and although i put it back on it kept coming off instantly, as soon as tried to peddle. i looked at the rear gears and noticed the top 3 (the bigger ones) were very wobbly, it looks like they have a thin spacer between the gears which i assume keeps them separate and from rubbing but the top gears had play and looks to have the spacer missing, possibly broken off between gear 7 (if that is the bigger one nearest the wheel) and the wheel itself, so it wobbles and also gear 6 & 5 wobble, so when trying to change to one of these the chain just slips between the gears and stops me riding.
It also looks like the little gear wobbles, but 2, 3, & 4 seem solid like they should be. the wheel bolts seem tight.
Can i just replace the rear gears? how do i know what size?
the bike is a gt aggressor mountain bike with 21 gears 3x7 , maybe from about 2010 but very very rarely rode until last year lockdown started.. i would like to keep it as it was won in a competition and is very light, and a nice ride generally..