Being "used to" something means that you are accustomed to it (a state). "Getting used to" something means you are *becoming* used to it (a process). So, it's possible to say "it took me a while to get used to speaking in English, but I am used to it now."

I agree with Kevin's explanation.  I made resources about a similar topic that could help you out:

http://www.enupgrade.com/troubleshooting/2014/5/27/used-to-to-be-used-to

Thanks for your answers ! :)