Your connection to the tv via chromecast should not consume any of your bandwidth to the internet. Your data cap is for internet usage. You are making your own ad-hoc network within your own devices, independant of the internet, so therefore no internet data usage.
Now, if you are watching youtube videos from the internet, and broadcasting then to tv, yes, you will be using your data. If you are using a Dvd player on the pc and showing on tv. No. Do you see the differences in data usage?