That's not a side effect I've ever had - in fact I had the opposite problem when I first started taking them. Have you tried licorice (DGL)? It can be helpful for some people with GERD, but it's also a mild laxative, so it might be worth a try.
Have you been given any advice regarding fibre intake - you may need to change your diet. Try eating less wheat if you can - the very high gluten content of commercial bread can make some people constipated. Stewed fruit may help too - apples, pears, plums, prunes etc (if you can tolerate them). Syrup of figs (like Califig) is good as a temporary solution.
If you can't resolve this issue within a couple of weeks do go back to your PCP/GP - may be worth trying a different ppi. And, of course, if it lingers, you would need to be sure it is purely a drug side effect and you might need to prove that by taking a short break from the drug. Otherwise you're going to end up with investigations to check your colon etc is OK!
If it was something that occasionally troubled you before, it may be worth another visit to your doctor to get things like thyroid function checked.
Hope it settles soon - some problems do sort themselves out once you've been on the drug a little while.
New stuff: GERD. Interstitial Cystitis
Lifelong stuff: Food allergies, eczema, asthma