No. The 11 ounces exceeds the TSA guidelines. Finish the drink before you pass thru security.
You can pass thru security with an empty water bottle, then fill it up in the waiting area (from a drinking fountain) and take that with you into the plane.
My carry on is 15"x11"x10" . Is this acceptable?
If you have a prescription for it, yes, but not otherwise.
nope