Do you know if she normally only peed a little bit?? If not, you may want to take her to the vet. I don't think being in heat would cause this problem, and it could be a bladder infection or urinary tract infection, especially if she's whining. Is she whining before she goes out, or while she's using the restroom? If she's whining before she goes out, that's her way of letting you know she has to go. If she's whining WHILE using the restroom, you should definatley see a vet. I would anyway since she's going so often and in such small amounts.
Also, since you've only had her for a day, it could be the stress of being in a new place that's causing this. I'd wait a couple days to let her settle in. If that doesn't solve the problem, call a local vet and see what they recommend. Also, watch for blood in the urine if you can. That's another indicator of a bladder infection or UTI. Best of luck to the both of you!
One other thing, if she hasn't been already, have her spayed. In the long run, it's healthier for her, and can prevent any unwanted litters in the future. There are enough pit bull and pit bull mix puppies in the shelter. If you don't believe me, check petfinder.com and I'm sure you'll be amazed at the number of pits and pit mixes you'll find.
Also, never ever leave her in your yard unattended. Pit bulls tend to have a higher prey drive then some breeds, and are jumpers. Should she see a squirrel, etc.. she could easily jump your fence (or just plain leave the yard if you don't have a fence, which you really should when owning a pit) and get hit by a car, etc... The other reason I say not to leave her unattended is because of the chance of a stray dog coming into your yard.
I also mention it because there has been a lot of problems with people harming and/or stealing pit bulls out of their own yards if they're unattended. Pit bulls are stolen, poisoned, and killed every day by being in their own yards unattended. Not too long ago, a pit bull by the name of Gage was shot by his owner's neighbor through their fence. Gage was on his side of the fence and minding his own business. Sadly, it's not uncommon for this to happen with pit bulls, due to their horrible reputation. Best of luck, and congrats on getting her, they're a great breed so long as you've done your research and know what you're doing!