Have I fried my Arduino UNO?
The reality is that you most likely did fry it. We can think about it this way: you supplied much more voltage to it than it was designed to handle, and now it doesn't respond to your computer. What other possibility is there?

The question now is: what exactly did you fry?  One thing that could very well be toasted is the ATmega328 chip. Whether you are in luck or not depends largely on whether you have an UNO with the SMD chip or the DIP ATmega328. If it is the former, and the chip is dead then you'll need to get a new Uno, unless you have advanced soldering equipment. If it is the latter you can buy a new  ATmega328PU and replace it in your Uno, however, even in this case the solution isn't necessarily easy.

The problem is that you'll need to get a bootloader onto your new ATmega328PU, and without an Arduino or an ISP programmer this isn't easy to do. Fortunately, ATmega328PU with bootloaders already on them are sold on ebay for just a few more dollars than the bare ATmega328PU which runs about $3-$4.

It could also be the case that other (non-MCU) components are damaged either instead of, or (worse) in addition to the MCU: the USB interface chip, voltage regulators, or any of the many passive components that are directly connected to the +5 rail. The trouble is that even with a multimeter it may be difficult to assess the damage. For my money, the best option is to buy a new Uno and move on, however, if you are interested in a (potentially complicated) project, at least the schematics are available. So you would want to look at the schematic drawing and test at least  every component that is connected to +5 and ground. Then you might want to test every component connected to those components, in case the blown out component shorted out something else. In the end you might have to test everything. 

The alternative strategy would be to assume the best, and look, and maybe try to smell the damage, and replace one or two components that look suspect, and then pray for the best.