You can use circular needles (the kind with a cord in between two needle tips). You'd be using them like straight needles -- turning your work at the end of each row instead of working in the round. The cord will not only accommodate the larger project, but will be easier on your wrists because you'll be able to rest the work in your lap instead of having it weighing down the length of your needles (as would be the case with straights).
There is no right way to knit; there is no wrong way to knit. So if anybody kindly tells you that what you are doing is "wrong," don't take umbrage; they mean well. Smile submissively, and listen, keeping your disagreement on an entirely mental level. They may be right, in this particular case, and even if not, they may drop off pieces of information which will come in very handy if you file them away carefully in your brain for future reference.