coriolis
To add a bit, what you say about a L in front of you and a H behind you if you stand with your back into the wind is true if you are close to the equator, where coriolis is weak. There is a L band close to the equator (the ITCZ) and wind from noth and south blows directly toward it. Wind directly from H to L is called Antitriptic wind, these are the monsoon winds.
There is another force present on higher latitudes, centrifugal force. When isobars are curved, so around a H or L on higher latitudes, there is resultant centrifugal force. Directly in between H and L, isobars are straight. Here there is no resultant centrifugal force, this is the Geostrophic wind.
There is a formula for this: (not required for the atpl exams) Geostrophic wind = PGF/ ( (2)(earth rotation)(rho)(sin latitude) )