We can't diagnose on here, but us diabetics are rather vulnerable to lovely things like fungus, which can turn nails yellow and thick, sometimes crumbly/breakable.
Don't muck about with them yourself, especially since tools used can contaminate other toes as well. You might want to see a medical pedicurist or a podiatrist? Between those two your toenails could get a heck of a lot healthier, regardless of what's going on with them. Don't know whether ou need a referral from your GP, but I asked for one through e-mail, and got it.
Good luck!
Jo
PS: I don't know about over there, but here I get most of my pedicure's sessions covered by my medical insurance, because I'd diabetic and the podiatrist signed off on it. Instead of 45 euro's, I pay 10. (Well, 15, with the tip), and I see mine every 5 weeks or so.