Even though I am a prime member why am I getting charged around $6 for shipping?
Do you see a gold box by your address asking you to verify it?
If so, click it.
If it doesn’t help, here are a few other things to try:
Log out of Woot and log in using the Login with Amazon button
On the checkout page, check “use this address”.
If you are using Microsoft Edge, switch to Chrome or FireFox.
Clear cookies for Amazon & Woot.
Allow cookies from Amazon & Woot.
Allow pop-ups; turn off pop-up blockers.
Log out and back in on Amazon, especially if you’ve changed anything there (e.g. cards, email, etc.)
Try an incognito or private mode in your browser.
(Please note: I don’t work for Woot, I just volunteer to help out here on the forums.)