i forgot my friends birthday and i feel awful

so i just recently remembered my friends birthday and it was on New Year's eve. it is now february. i feel absolutely awful. i've done this twice now, to both of my friends and i feel like a terrible person bc they say happy birthday to me and i completely forget theirs. i feel to embarassed to message them now and say "hey i'm so sorry that i forgot your birthday, let's do something the next time we meet, my treat". albeit we only see each other 2 or 3 times a year bc we are all away doing our own thing, them at uni and me trying to decide on a career path.

i am a summer baby so i think i just got used to people never remembering my birthday, so in turn i never remembered theirs, and i just think that this carried onto into my late teens. i say i'm going to remember and i ultimately forget. i can't help but wonder what they think about me. we have a group chat but i know that they message privately too bc i do sometimes with one of them, but i just have a feeling that when i forget that they talk about me like "oh she forgot again" and i just feel horrible. i probably am overthinking it, but i asked my parents and they said, "well how would you feel if a close friend didn't say happy birthday? that's probably how they feel".

i don't really know what to do.
does this make me a bad person?