When my hubby and I were trying for number 1, I woke up one morning [2-4 days before my expected period] and couldn't get my contact lenses in. My eyes stung and burned so bad when I tried putting them in. I remembered a woman saying she couldn't wear contacts during her pregnancy because her hormones caused major eye dryness, so I took a p-test (well, three crappy cheapie kind that came out blurry and faint, and then a digital test that said "pregnant" in black letters...no guessing! I highly recommend digital tests to everyone I know. Target sells a 2-pack for $10).
Some women say they feel fatigue and mild implantation cramping (milder than a period) before their missed period, too, so yes, I think it's possible to feel signs as early as in the first couple weeks after sex. Morning sickness, smell sensitivity, and major breast tenderness don't normally kick in until around the 6-8th week of pregnancy, or 2-4 weeks after a missed period.