If it's a university project, I'd recommend having a (positively worded!) talk to whoever set it, and finding out what they define as graphic output, and how they expect you to produce it in ansi C. There may be a misunderstanding here about what tools you're allowed, or what you're expected to do. Some people would regard a graph plotted merely as "*" symbols on the text screen as a graphical output...
There's no point in specifying ansi C running in dos and then not allowing you to use bios interrupts because dos itself is using them - i.e. they must be there! Since you're already non-portable (must work on dos) there has to be some allowance for non-portable code. Perhaps if you can wrap up all the non-portable stuff in one easily-maintained chunk and put all your ansi-standard stuff in one easily-ported chunk?
Good luck, anyway. Otherwise it does sound like an impossible mission.