Is it possible?

It possible to be pregnant even after you've had your period? Cuz I've had some weirs stuff happen lately. Like 2 days ago, I puked for no reason. Yesterday, I puked after eating mango peach salsa with chips, and I never had that problem before. I haven't took a pregnancy test cuz I thought it be wasteful cuz I just had my period on 1/22/16-1/26/16, which is also kind of a short cycle for me. I'd love to hear anyone in put.