How early do pregnancy signs start?

Hello! I had sex on the 10th and 13th and starting about the 16th I began to have nausea almost constantly and have felt exhausted. I haven't had fevers or anything so I know it's not the flu. In addition I have noticed stuff that usually smells good to be has smelt very strongly and bad. My husband is convinced I am pregnant but I know a test wouldn't show up this soon. Would my body respond to pregnancy this soon? Is that possible?