Welcome to Reef2Reef, and sorry for your troubles!
The "worm" in question seems to be a brittle starfish (an Ophiuroid) - these are almost always harmless/beneficial in our tanks, and almost certainly not the cause of the problem you're facing with your coral.
Can you give us some information about your tank for us to help figure out what's wrong? The information below would be helpful:
-Water parameters (nitrate, phosphate, calcium, alkalinity, etc.)
-Lighting (what specific lights do you have, how much PAR does the coral get, what is your lighting schedule, how high above the water is your light, etc.)
-What kind of flow is the coral getting (wave makers, filters, pumps, etc.)
-Tank age (how old is the tank?)
-Picture of the whole tank under white light
-Tank inhabitants (what fish and invertebrates do you have in the tank)
-Are any other corals or tank inhabitants having issues?
