Non-design background to Masters in ID

Thanks for the inputs guys! It means a lot!
I am working on my sketching skills and will do as much as possible within the deadlines. I have a quite a bit of experience in designing websites(and coding)…and almost a years work experience in UX. Will this help my application in any way?

I have been reading through here and on school websites…and collected that Illinois Inst of Tech, Georgia Tech, Pratt, Arizona State Univ amongst others have 3 year programs. Auburn offers a PostBacc Environment Design course before applying to ID. Which of these might have the strongest foundation courses but are yet attainable by someone with relatively weaker background? I am willing to put in as much effort as possible to sketching.

If these are all beyond my reach, please let me know some colleges I can apply to that might have strong 3 year courses. Thanks a lot.