There seem to be two main schools of thought regarding Plantar Fasciitis. One is very well represented above already: the one that recommends extra support in the middle of the arch by wearing supportive shoes and orthotics to help relieve the pain.
The other school of thought is quite different and focuses more on doing exercises to strengthen/stretch the foot and wearing flatter, more flexible shoes.
Given that gymnasts aren't able to wear supportive shoes while competing and practicing, I believe that it's important to at least be aware of the second school of thought and consider what they think as well, regardless of what you end up deciding on (preferably with the help of a qualified professional if it continues getting worse).
An article outlining the basics of treatment recommendations from that school of thought:
http://www.somastruct.com/treatment-of-plantar-fasciitis/
A page of various links about natural food integrity and gait gathered by a sports podiatrist from this school of thought:
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