Welcome to TE.
Sounds like we're the same inseam but I'm slightly taller at 5'1/2". I won't bore you with the details of my bike fitting experiences but after 4 road bikes that didn't fit I found a very good bike fitter and built a custom frame. It's my "Cinderella Slipper" so to speak but it took many years of trial and error to get to this point.
Besides being "vertically challenged" I also have small hands, narrow shoulders, short arms, short femur and a longer torso all of which contributed to my bike fitting woes. I spent years trying to figure out why my bikes weren't comfortable. When I started working with bike fitters (all of mine were Serotta trained) I learned my needs and eventually decided to do the custom bike.
If your frame fits there are a lot of things that can be done to improve your fit. IMHO, having another eye to help you understand your needs goes a long way to getting a "Cinderella Slipper". A good bike fitter can help you with this.
Keep reading this forum, there's lots of information here on bike fit.
Rereading your post 11" does sound small, my mtn bike is 14". However, good bike fit has more to do with top tube length than standover height.



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