Yes, your worn out tires could definitely be the cause of your vibration. Perhaps you should slow down a bit until you can get them replaced.
Warped brake rotors
How long has it been since you did brakes ?
The tires may be contributing to this but I dont think thats the whole issue if the vibration was constant and felt through the steering wheel then yes a wheel may be out of balance. but since it is only felt during braking and at high speeds the front disks of the car may be slightly warped or a brake caliper is sticking. You wouldnt notice this stuff in lower speeds unless it s pretty bad. and yes brake rotors can become warped VERY quickly especially if cheap pads are used and not changed when needing replacement..
I have a Honda Accord 2010. Today while driving on the highway I experienced vibrations when I applied the brake @ 70mph. I didn't brake hard but it was just to slow down the speed a bit. I could feel vibrations in the steering wheel and there was some sound coming. Even my friend sitting next to me felt the vibrations. I tried the same when the car was at 60mph and couldn't feel a thing. My tires have worn out and need to be changed. Can that be a reason for this issue or is this something else. Would like to mention it has 64Kmiles on it right now.