As you have read, you cannot get an accurate diagnosis on the internet. School trainers have more information than you do, but they have limited diagnostic knowledge and are not health experts when it comes to injury.
If you want to be able to run competitively, long term without aggravating your condition, check with an orthopedist or a podiatrist (foot doctor) who specializes in running or sports medicine. A new stress fracture will not necessarily show up on xray as it can be too small to show until some healing or callous formation develops. Your doctor will know if you need further workup.
Also, a sports doctor would be able to evaluate your foot to see if your have a structural or functional problem with your foot as it relates to your running. Or they may refer you to a sports physical therapist or recommend orthotics (shoe inserts).
You describe mid-foot pain, not heel pain. As to plantar fascitis, the pain is usually noted at the heel on the bottom of your foot where the fascia attaches.
Often, pain resolves with corrected technique and/or more appropriate shoes. Check out What should I look for in a running shoe? to help you in choosing the right shoe. And check out these answers to help you understand other possible causes and solutions to prevent pain when running. Hope this helps.