How to use Polish past tense "byłem" vs "byłam" correctly?

Hey everyone! I keep getting confused about when to use byłem vs byłam in Polish. I’ve noticed Polish YouTubers use different endings when talking about the past.

From what I understand, it depends on the speaker’s gender — byłem for men and byłam for women. Is that correct?

So if I’m a woman, should I always say byłam w sklepie (“I was at the store”), and a man would say byłem w sklepie?

Just want to make sure I’ve got this right — thanks!