Yes, I go through this all of the time. Honestly, everytime I finish a piece I feel like I can't come up with anything else. In fact, I am going through it right now, while I sit here and scribble crappy thumbnails that look like crappy thumbnails. It always works out in the 11th hour, but this continual cycle of mysery isn't fun.
However, when I push through I always learn something new, and so in some ways I am addicted to it. The only time I didn't have anxiety about my art was when I used to think I was really good, and never tried learning new things.
Here is my process of overcoming my anxiety
1- tell my wife that I suck at art, and I should just quit, and she always begs me to continue on and tells me how good I am.
2- tell her the same thing a couple hours later, and she really emphasizes that I am good enough.
By the end of the week I feel so creative, and then will go through this all again the following week. At some point my mom will catch on.
Though some of my steps are a bit dramatized, it is usually something along those lines how I deal with my anxiety. I also make sure I have people to get advice from, such as here on the forums. Everyone here has been support group for me over this last year, and they all are so encouraging, and I believe we all want each other to succeed.
Hope that helps...probably not though...I suck at this kinda stuff.