Can you get frozen food? I use the following. Mysis Shrimp, Krill and MArine mix. I dont recomend Brine shrimp as it is practically nutrient free.
If you have a tang then i would suggest green stuff as they are mainly veggies. You can purchase dried seaweed for the tank and this can be clipped to the tank to allow the tang to feed.
I would not use bloodworm unless its a last resort as its not a natural food. I have used it in the past to get difficult fish to feed and it does seem to work but i would prefer to give them a natural and cosnistant diet of what they would feed on normally.
A seprate tank for the tang will help but only for the short term as 20 gallons (us) is still too small. In another forum i use there is a member with all sorts of problems with his tang and he has a 75 gallon tank (uk gallons... so roughly 90 US gallons).
What you must consider is the lifestyle of the fish you are caring for. Tangs are open water swimmers and have huge territories. They will travel for miles just grazing the rocks for algea in their natural state.
They are also an extreemly easy fish to stress. This usually means they will come down with whitespot or some other illness and die, this ilness in turn will infect other fishes and thus you get a tank wipeout.
I used to have a video footage of a tang that was kept in a tank that was too small and was driven mad by this. It spent the entire daylit period just performing somersaults in the tank as it was so stressed by its cramped envrionment
If i can fins this footage again i will post the link.
You say your parents will not allow you a 100 gallon tank. but they will allow a 2nd 20 gallon? how about they allow you to get rid of the 10 gallon and up the 1 tank to 30 0r 40 gallons as a comprimise? Still not ideal but it gives the tang some growing room and in this period you might be able to find someone willing to swap or trade for something more suitable?