Saw my neighbor naked and my mom caught me, should i apologize?

I live in a house and its very close beside my neighbors house, and their bedroom window is about 8 meters roughly from my bedroom window. For the past month i noticed every night my neighbor comes home she probably hits the showers and changes in the room, i think she lives alone because i don't see anyone else there at all ever., so basically every night when she comes home from work i use my binoculars and peep her (i try not to but im a guy and an only child) and she usually walks around bare naked and stretches and stuff before she goes int othe shower shes like 35 maybe, and she bends over and all sorts of stuff and i watch, but yesterday my mom came in the room like a snake quietly and saw what i was doing and she started yelling and hitting me, and she told me to apologize to her this week or else she will tell my neighbor. What should i do im so embarrassed, should i lie and tell her i already apologized to my neighbor?