Aiptasia can becontrolled with peppermint shrimp but my experiences, it was hit and miss. Could use Syringe to suck it out rather than inject chemicals into it.
As far as adding one fish, dont have problem with that idea as long as avoiding territorial fish such as tangs. Since only 20G, could have one baby/juvie tang provided willing to accomodate properly as they grow.
As far as Damsel, if you saw it being stung by aiptasia, no arguments there though I've never seen fish get stung by aiptasia/
anemone as any alert fish will avoid such danger.
Only time I actually saw fish die from such stung was when tomato clown which was spook by simple tap on glass somehow got stung by Cerianthus (not me) as dashed around the tank.
It sounds like fish is very nervous for whatever reason. Could it be because he/she is w/o any tankmate?
Hopefully does calm down and feel at home as tankmates are added.
I dont mean to add another damsel since these particular damsel can seem to tolerate each other (especially 2 in such small quarter) unless match made in heaven!LOL!
Hope all goes well!