Now, my doctor doesn't even have an X-ray machine,

Your GP will make an appointment for you at the local hospital for your X-ray to be taken there. You will probably be billed for that separately and in addition to the fee your GP will charge you for the other parts of the medical exam.

She reluctantly agreed-so right from the outset before I even start the job we have bad feelings.

If you haven't signed a contract yet, I guess from what you have posted that you and your FAO to-be won't be signing it in 'the spirit of mutual friendly co-operation', which could invalidate the contract???
Female FAOs in China can be vindictive. Personally, I wouldn't take a job at a school/college that has one unless I had no alternative job offers. They can be out and out bitches!