Nope. :D You are almost right. :D
나를 도와주십시오! = 나를 도와주세요! = 도와주십시오! = 도와주세요! = Please help! (Polite form)
나를 도와줘! = 도와줘! = Help (me) (Casual form)!
도움 = help (as a noun)
도움이 필요해요 = (I or we) Need help please! (Polite form)
도움이 필요해요 = (I or we) Need help please! (Casual form)
돕다 = to help (as verb)
도우미 = helper
EX) 주부는 가사노동을 합니다 = A housewife does household chores.
"도와주세요" will be right for almost any situation. If you are in danger, "살려주세요" (lit. Please save [my] life) may also be good. "도움해주세요" is kinda weird form, but Koreans will help you anyway.