I have a subscription for Shop. I cannot access the program. When I try I end up with Free.
Sign out, close the browser, reopen it and sign in again. Are you sure you are getting SketchUp Free? They look a lot alike.
Make sure to use the same email for signon as you used when getting your license.
When you do get to SU Shop, you can see the absence of the Sketchup watermark in top right of the drawing window.
If you still see the watermark, you are still in the Free web version.