Is your business mileage not simply reimbursed by your employer?
If not, presumably you get a refund from your self assessment? Is that is the case then you will just get back less for 13/14 rather than owing some to Hmrc. Unless you have some adjustment to your tax code (check the notice from HMRC to see if there is mention of this), in which case you may owe some cash.
Pretty sure the hospital mileage can’t be set against income I’m afraid as it won’t count as business mileage, so Hmrc won’t be interested.
Sorry that you are unwell, must be tough for it to hit in the pocket too. Might be worth asking any charities/support organisations related to your condition if they are aware of any schemes that offer financial support.
NHS does offer some help, but it is means tested:
http://www.nhs.uk/nhsengland/Healthcosts/pages/Travelcosts.aspx