A new tip,even a cheap one, properly cared for should last you a few 30min soldering sections before dieing on you. If you have a new tip, try that, don't bend or pry with the tip either, it cracks the coating. If you tend to solder a lot, or for long periods of time, I suggest a quality iron. It will keep you from pulling out your hair. It really is a big difference in how well they work.

The only people who I have heard say lead free isn't all that bad to work with, have never used lead solder, especially 63/37. I can't stress enough how much better 63/37 is over 60/40. Its not as huge of a jump as lead solder vs lead free, but once you use it, you will not want anything else.