Grad applications: mediocre grades from an ivy league (top 10) and outstanding grades from a smaller school; what should I do?
Just apply and see what happens.  You can't change the past.

Typically a graduate application will explicitly say that you must submit transcripts from all universities you have attended (or "earned credits from").  So it is not appropriate to simply pretend that it never happened.  

Grad school decisions would, in any case, be based mainly on your more recent work, so the first year of your studies will not carry much weight regardless.  I'd ask the question: considering students at your current institution whose records in their later years are similar to yours, are they successful at getting into grad school?  If yes, then I think you are in good shape.

There is no systematic procedure in graduate admissions for discarding grades that were affected by medical issues.  You can, if you wish, discuss the issue in your statement of purpose (or other similar essay), and it would be up to the admission committee to decide how to take that into account in considering your application.  However, my feeling is that you don't need to say much more than "I started at University X, it wasn't a good fit, I transferred to Y.  Now here are all the fantastic things I've been doing at Y..."  

As you get ready to apply to grad school, you will want to have serious conversations with your faculty mentors. This is definitely something you should discuss with them (though you don't necessarily need to go into as much detail as you did in this post), but I suspect they will agree that it isn't a big deal.