Yes, you can have a gall stone problem without a gall bladder because not every surgeon removes the bile duct, if I remember correctly. If they don't then you could still have a stone lodged in the duct. However, since gall stones are only made in the gall bladder, you can't produce any more; if you have one, it's been leftover by accident (which means if that's your problem, it can be fixed and won't manifest itself again).
A lot of people, though, have "phantom gall bladders." Even I sometimes hurt right where it used to be. As far as I know, this is just a tingling sensation of the nerves--same as people who have had a limb amputated.
I had two different doctors put me on antiacids when my gall bladder was bad and they never made a bit of difference; I might as well have been taking a sugar pill. Of course, if you actually have ulcers, you will need medicines, but are they sure you have ulcers, or do you just hurt in your stomach region, so they think you have ulcers? You may just be having gas pains/cramps in that region instead.
My G.I.'s Nurse Practitioner told me that excess bile from not having a gall bladder could manifest itself in two ways: it could go down and cause diarrhea or go up and cause acid reflux. For most people it goes down most of the time, but you may have yours going up. If that's the case, regular antiacids may not help because bile--as I understand it--is much more acidic/concentrated than regular stomach acid, so you may need more potent medicine or a stronger dosage to tame it.
Then there's the usual recommendations I give everyone who has a bile problem: give up caffiene and lower your fat content. That helped lower my bile production to manageable levels. Mind you, mine goes down, but I would think it would work for going up as well.
Also, try to eat more frequently to keep your stomach from sitting there with nothing in it but acid and bile and avoid acidic foods like orange juice (all of which your dr. probably recommended already).