My experience of Levemir is that it doesn't sting, so I'm afraid that I'm not much help in this respect. I'm also not aware of anything that should make it sting, unlike Lantus.
I have a pump so I don't use Levemir, but if it doesn't usually sting maybe you just got a bad injection spot? When I was on MDI, I found that some injections were a lot more painful than others. Most times they were fine but occasionally I'd get a spot that felt very sensitive.
See how your next Levemir injection goes. If you continue to have a problem, I'd speak to your DSN.