Yes, illness can really mess up the budget. My strategy at least for this year was to get the low deductible plan so that at least I could calculate my max out of pocket amount and budget for that, knowing that I'd meet it. The premiums are more expensive, but I like the predictability of knowing the max amount.
I also itemized medical expenses this year for the first time. I think you can deduct anything greater than 10% of your AGI. If that could work for you, keep track of everything, including mileage to/from appointments. And you can include vision and dental costs as well.
If you end up owing a big balance, I've heard that you can also negotiate a lower payoff amount if you pay off the balance in cash on the spot...Haven't done this yet myself, however.