My running shoes are making the back of my ankles bleed! But I have to go running! Help?

So I run/workout a lot and my old running shoes were really worn down (they were Nikes). So I bought a new pair of Pumas. At first they were super comfortable, but I noticed they irritated the back of my ankle a little. I figured it would go away, but instead it got worse! Now I have these sores on the back of my ankles. I've tried wearing longer socks (didn't work and it looks lame) and band-aids (they don't stick well). I can't even walk in them now! I guess I could wait like 3 weeks for my ankles to heal, but I have to workout! I can't buy new shoes either. Please help!!!!