Has anyone started their period and still be pregnant?

My period was extremely light and was short.

I was sent home from work for throwing up at work and these next two days that have followed I’ve been extremely nauseous and had to fight getting sick every single time I eat.

There’s no fever and nothing else to indicate that I’m sick.

I haven’t tested or anything because I figured if I started my period there’s no reason? But now I’m beginning to wonder if I should😭

Any advice is welcomed🤮😭😷