Jameth: The problem is, around the time I would normally start braking, a car came up beside me fast in the adjacent turn lane, and took my attention away as I turned to look at this car to determine whether they were going to turn in front of me and cut me off. I wound up locking up my brakes, fishtailing, and going over the handlebars.
What you describe is all to common in the USA. A US style poorly designed crap piece of bicycle infrastructure. Poorly designed because were the path meets the road there is a very lousy transition for a bicyclist. The motorist in the adjacent lane next to you is driving in a predictable manner as they always do on the road and possibly clueless to your presence. You haven't given any indication that the motorist was in any way in the wrong.
I rarely ride on any kind of bicycle path because I consider them even more dangerous than the road in most situations. It is the intersections were the most incidents happen even on the road. and were bike paths, mup or others meet the rode there is very often no traffic controls for anybody. They place you out of sight and out of mind. You knowing this need to adjust to each situation and practice due care. I can only guess as to how you crashed other than your words. send some pictures of that location or direct us to the names of the roads so we can look it up on google maps might help.