Dear Lily,
First I have to say: I am very happy that you are considering this so early! I am a professional nurse from Austria, and I worked for some years in Shanghai. I have seen unbelievable things such as managers travelling to China without their medicines, thinking they could easily buy them locally. (No, they cannot!)
I'm wondering how I will cope in China since they often use sesame oil to cook there food?
You are right: Most dishes contain sesame oil for adding flavour. If you order food in a restaurant, you have to make very clear that even the rest in a pan that has not been cleaned can cause a severe reaction. So, to cook for yourself is probably the safest way.
Does student accommodation have self catering or would I have to rent somewhere privately?
The rooms in the dormitories of the universities have no kitchenette or so, but you can rent a fully equipped apartment for little money (if it is not in Beijing or Shanghai – these cities are expensive).
Are there plenty of foods in the supermarkets that I could eat?
Yes. You can also go to the farmers' market and buy fresh vegetables and fruit. Cheaper and better to learn the local culture
Should I completely avoid restaurants or is there anywhere that would cater for me?
You should avoid the big chain restaurants since they have prepared food, and even the stuff working there probably does not know if it contains sesame oil or not. Small restaurants which prepare food freshly for you should be okay, but you have to make very clear that they have to use clean pots / pans / cutting boards etc. for you. This depends on your level of spoken Chinese...
If I had a bad allergic reaction would the hospitals know how to deal with me? Are there any cities that would better suit me? Any general advice?
The hospitals will know, don't worry! The bigger problem is to reach the hospital... the emergency services are very poor, and the emergency line can only speak Chinese. The emergency call is 120 for ambulance and 119 for fire brigade, by the way.
I strongly recommend to get a SOS Card for you which has been invented by expats at the Hangzhou International Fellowship (HICF), and now, via the fellowships throughout China, covers all major cities (and far beyond, as the Chinese fellowships have introduced the SOS Card all over the world...). Just look up “The SOS Card Project”. (Or send me a private message if you cannot find it.) You can read the page “A short history of The SOS Card Project” to get the background.
This will give you an emergency ID **and** plenty of useful information on the situation in your destination, such as, good hospitals, dentists who can speak (a little) English etc. And a first contact to the local fellowship as well
Greetings from Austria,
Liese