Your raise size preflop is far too small, it accomplishes nothing but lure everyone into the pot. You set yourself to play a big pot out of position vs multiple opponents, never a fun spot even when you hold AA. Raise to 15BB preflop.
I would check/fold the flop, a speculative backdoor draw to the 2nd nut flush is not good enough for me to continue.
Turn and river are a bit irrelevant I would say, errors were made on prior streets.
I think the important factor is you have to know QQ doesn't do well multiway so you have to reraise larger preflop. Then just cbet this flop because its good in general for your reraising range and is easier to play that way postflop. That's if it were heads up (like it should have been). But given this is 4 ways im agreeing with a check fold because you really only are beating a bluff and you don't have quite enough backdoor to help you out.