Yes. As you're discovering, your belly isn't the only thing that gets bigger during pregnancy! This is partly due to pregnancy weight gain and swelling from the extra fluid your body retains while you're pregnant (called edema). To ease the swelling, soak your feet in cool water and prop them up as often as you can.
But there's another reason that feet seem to grow during pregnancy. The aptly named pregnancy hormone relaxin, which loosens the joints around your pelvis so your baby can make his way down the birth canal, also loosens the ligaments in your feet, causing the foot bones to spread. Your foot bones aren't actually growing — it's just that the ligaments that hold these 26 bones together aren't as tight as they were.
You may notice your shoes getting a little tight as early as the second trimester, and they may continue to increase in size until late in pregnancy. While the foot swelling generally subsides within a month after delivery, any foot spreading caused by looser ligaments is permanent. I estimate that half the moms out there wear shoes a half or a whole size bigger than they wore before having babies.
The bright side, if there is one, is that you get to buy new shoes! Buy a few pairs of comfortable, roomy shoes to wear during your pregnancy, but be aware that you may have to go back for more once the swelling settles down and your shoe size stabilizes about a month after delivery. Whatever you do, don't try to make do with your old shoes! Wearing tight shoes can aggravate bunions and cause a host of painful foot problems, ranging from ingrown toenails to corns and calluses.
Finally, since feet tend to grow with each pregnancy, you may want to hold off on those pricey Jimmy Choos or Manolo Blahniks until you're finished having babies.