Different vocal ranges that change in song?

I like to sing songs by men, who sing in falsetto like Darren Criss and Charlie Mcdonnell. But when i sing along to the song, either my voice is really low (not as low as the singer) but in mid song i change to a high pitch, and then back again. I don't sing professionally, I just do it for fun and i can perfect notes, its just weird. is it weird to sing songs my men if your a woman? My pitch tends to change when its a different song, is this normal?