For a majority of your life, like many people, you've probably worn shoes, especially when doing anything that involves physical exertion or significant use of the feet. You say you've only been barefoot running for a month. So the most likely scenario is that you've unwittingly overdone it.
From Naturally Engineered - Pain and Swelling in Foot From Running Too Much Too Soon:
The obvious reason is that the bones, tendons, and muscles in your feet are not conditioned to handle running many miles without padded shoes right away. All of that tissue is severely underdeveloped from a lifetime of wearing shoes.
There are 20 muscles within our foot and 12 muscles from our leg that attach to our foot. According to Dr. Michael Nirenberg and Dr. Benno Nigg, while walking in shoes, only the tibialis anterior (a shin muscle) and triceps surae (calf) muscles are needed. When you start a barefoot or minimalist training regimen, all of those parts of your feet which have stayed asleep inside of your shoes are now awakened and exercised quite rigorously. If you don’t proceed slowly you are more than likely going to encounter some pain.
You say you've already encountered some pain, and pain can lead to swelling due to damage to the previously underdeveloped soft tissues in your feet. While the pain going away is a good thing, the swelling is a sign that you should still proceed with caution.
From Today's Health Information - Swollen Feet:
If your foot is hurting and you keep barefoot running on it, your foot may swell. My advice is to avoid running on a swollen foot. It needs to heal.
If you don't overdo it as you are beginning barefoot running, and you take care of any pain right away by giving your feet a break, and then give them an ice bath several times a day, you should be able to avoid most instances of swollen feet.
One of the things you can do to help prevent as much damage as possible is to ice your feet and ankles. This will also help reduce the swelling. Keep in mind that, according to Natually Engineered, some pain early on is common and is to be expected. Here is their advice on how to proceed:
You may not be able to avoid all injury or pain as you are getting started; when I began barefoot running, the cartilage in my forefoot broke apart inside my foot. This may happen to you, too. But you can minimize the damage and pain you experience during this process by following the advice above.
The other thing you can do to avoid or minimize injury is to put your feet in a bath of ice water immediately after barefoot running, every time.
In summary, it's wise to proceed with caution. Listen to your body carefully. If you start to experience more pain, it may be a sign to take it easy, use more ice, pay attention to your form, or even take a break and give your feet time to completely heal.
If the swelling doesn't go away on it's own or if the pain comes back, it may be wise to seek medical advice, just to be on the safe side.