how to know about designed airways above my house
Airways is a term that is used for the sort of "highways in the sky" that a lot of commercial air traffic use. 

However, as you are reasonably close to an airport what you're most likely referring to is SIDS (Standard instrument departures) or STARS (Standard terminal arrivals). Both of these can be found quite easily by searching for the airport name/identifier along with those 2 terms

One such example is here: https://v1aviation.co.uk/wp-content/uploads/2016/10/LIMC.pdf

It is a long document with a lot of information, however around page 19 you start to see some example departure routes from one of the northerly runways, which do indeed turn east and west depending on the route the aircraft is taking. You might recognise some of the local topography and be able to estimate where your house is based on local knowledge.

Edited to add: The screenshot you have added looks similar to the easterly departure from 35L.



However, as pointed out in comments, the actual departure of that flight was from 35R, so the SID followed is likely to be the one later on in the linked PDF (pp 23-onwards).