Chafing is one of those by-products of running that can really deter your training plan and put a damper on your desire to get out and run. It is one of those injuries that is seemingly quite minor, but results in big pain and can be really difficult to push through! Chafing on the inner thighs is especially tricky. Chafing under your arms is still painful but you can hold your arms at a different angle to avoid contact. Unfortunately, you can't really drastically change your gate and stride so much to avoid chafing.
The first thing you should do is wash and sanitize the area. You will want to avoid bacterial growth in the chafed area, which could result in a worse infection. Take a hot shower, pat dry (do not rub or risk worsening the pain) and then soothe it with a lubricating and thick diaper rash cream like Desitin. This will help treat the already-existing chafing you have.
Then, to prevent your chafing from getting worse, make sure you are taking the necessary steps to ensure your skin stays hydrated. Chafing happens when moisture accumulates on dry skin and is rubbed by clothes, your own skin, another object, etc. You can avoid this by getting rid of your dry skin. Make sure you are drinking plenty of water and fluids throughout the day, and use a heavy duty moisturizing lotion twice a day - once in the morning and once at night. Also try avoiding running in just shorts. When it is hot out, or if you are training on a treadmill, this might not be as comfortable. However, wearing protective clothing will stop your legs from rubbing together. Also, use a good anti-chafe cream, gel, or lotion. There are a lot of great options on the market, and a list to help you find some can be found here. Just lather up the areas of your body that are prone to chafing before you head out and it will provide a protective barrier from the dry chafing.