Hi, I'm a pediatric physical therapist. It's very normal for some kids to go through periods of falling, usually as they hit growth spurts. However, there are some kids who keep falling, and they can often benefit from physical therapy. There are lots of mild physical problems, such as flat feet or a tight ankle muscle that can cause falling and can be easily treated. I would keep an eye on your child for a month or two and see if it doesn't improve. If it doesn't, you might want to get a PT referral from your pediatrician...it can't hurt. I also recommend you find a pediatric PT and not just your neighborhood PT. Often, a pediatric specialist can spot small problems that an adult PT may miss. Podiatrists are fine if you can tell there is a problem with the feet or legs, but they are not trained to spot some minor coordination disorders that can cause falling.
As far as shoes, the best shoes are not always the most expensive. You can find great soft sneakers at Payless. The most important, and hardest to find feature, is good arch support. For some reason, they don't put much arch support in most toddler shoes. Stride rite sneakers are great, but I've seen some cheap sneakers that are pretty good too. The other important thing about shoes is that they fit properly. I have met many kids who fall who are wearing shoes that are too big so they can "grow into them." Some kids fall less barefoot and some fall less with shoes, so try both. Good luck!