I agree with those (WSArabians in particular) who have stated that it is not the breed, it is the training, as well as the dog's handling potentially prior to being in your care.
I do dog rescue (specializing in Pittie and Staffies) and while a select few of the dogs we rescue do have some form of aggression issues, the MAJORITY of the Pits/Staffies we rescue do not have any issues, are good with other dogs, cats, small animals, kids, and people in general. We have adopted adult Pits/Staffies out to families with cats, dogs, and even human infants, depending on the particular dog being adopted.
Many people think that "shelter dogs" are basically "damaged goods" in one way or another. "Oh, he was dumped at the shelter because he was aggressive.... because doesn't listen, because he can't be fixed". That is far from the truth. While SOME of these dogs do come out of the shelters with issues and need training further than basic obedience/commands (whether it be for aggression, dominance, anxiety, fear, etc.), MANY do not.
Back to my point, while your girl is a Pittie, she is not acting the way she is just because "she's a Pittie". Unlike how many people think, being "a Pittie" does not mean that the dog will magically turn aggressive and dangerous. Being "a Pittie" means that they come with a predisposed negative judgement on their breed that is more often than not extremely FALSE. Like any dog, a good upbringing/"childhood", boundaries, socialization, obedience, and training are KEY to a stable, well-rounded dog. Unlike how many people think, you can't just socialize a dog while they are a puppy, then don't socialize them properly for years and expect them to still be perfectly fine going to the dog park with 20+ other dogs. Like anything, they need consistency.
Contributing factors for her current behavior could be the way she was handled prior to you getting her, the way you are handling her (no offence), or the behavior you are allowing her to get away with (again, no offence). Many, many owners can not see the "warning signs" (with ANY breed) in regards to bad behavior, the onset of aggressive or dominant tendencies, etc. Being able to pick up on, acknowledge, and stop these warning signs in time are very important.
I have been rescuing (officially) since 2008, but have been "rescuing" animals my whole life, and honestly, out of those years I have only had one Pittie growl at me... and that was after he was dumped in a parking lot at night by his owner and after getting hit by a hard while trying to chase his owner's car. I have been snapped at, lunged at, and growled at by many small dogs though.-- These numbers are not based on a small handful of dogs, but the many strays I have pulled off the streets, rescued myself, etc.
I definitely agree with whoever suggested watching The Dog Whisperer. You may be able to get some good ideas from those episodes. I also definitely suggest finding a trainer. Petco is okay to use if that is all that is available; however, you will probably find that they only cover obedience and commands. I doubt they will have a trainer who actually specialized in aggression. It is tricky finding a good trainer, as so many say they are good, know what they are doing, etc., but actually do not, and end up messing the dog up even more. Very FEW trainers (actually called "behaviorists") know how to properly acknowledge, understand, and correct aggression issues.
To start, get your dog's obedience down perfectly, if you haven't already. This will help TONS in working with the dogs aggression, or other, issues. There IS such thing as "leash aggression", in which the dog shows aggression toward other dogs (or even people) while on the leash, but is (usually) fine while off-leash.
Here is the link to my training tips page. Make sure to read the bottom portion of that first page, as it gives tips on how to find a good trainer. We have dealt with a handful of bad trainers and know just how hard it is to find a good one. The "proper dog-to-dog introductions" page, the "bringing a new dog into a home w/ an existing dog" page, and the "tips on helping prevent behavioral issues" page will all come in hand for you. If you search online, you will find many different ways to introduce dogs to eachother. The majority of the time while weeding through the different ways is to use common sense. "Is it a good idea to let the dogs be set free into the yard to meet for the first time?"... No!... "Is it a good idea to let he dogs rush up to eachother and meet nose-to-nose for the initial introduction?"... No!
Also, make sure to read the section on the proper introduction page on the signs of dominance and/or aggression ("warning signs"). Training Tips - LEASH Animal Rescue
The BIGGEST thing is to STICK WITH IT. Don't try to fix the problem for 5 minutes, then assume it isn't going to work. I have found this is a HUGE issue with people, especially people I have tried to help/work with. They are not open to trying new things and they do not stick with the training if it doesn't how 100% success withing the first few minutes or within the first session.
Good luck and let me know if you have any questions! Pitties are amazing dogs and are so misunderstood.