That's interesting. In Br English, although we do use 'inside track' like that, we use 'inside lane' in the reverse meaning; so that in both the UK and the US the inside lane is on the left. There is the related expression 'overtake on the inside', sometimes - informally, jocularly - replaced with 'undertake' (with a punning reference to its dangerousness*).
*Dangerousness, that is, in a country where most drivers expect traffic on their left to be travelling more slowly than them. In countries with a different attitude to lane-discipline drivers may expect to have to watch their backs!
PS There's also the word pair near-side/off-side, used to refer to the driver's side and the passenger side, as in 'near-side wing-mirror'.