Does this translation into English also mean "I'm wearing socks and underpants" or does this translation just mean that you habitually wear them?
Just habitually. Or you carry them (also habitually)
Today "Mam na sobie skarpetki" ( I have socks on me) , "Założyłam/em / Włożyłam/em skarpetki", I would say "Ubrałam skarpetki" but it is regional (I have put on socks. ). Jestem ubrana w .... (would work with dress, coat, suit, blouse and skirt, jeans and T-❤❤❤❤, bathsuit, etc., describes most important thing you wear)
Technically "underwear" is a wider term and it translates to "bielizna", but yeah, you can.
Majtki, we tranaslate to underwear. Underpants are the long underpants that grandpa use or maybe used widely in Europe