What can I put in my shoes(regular daily saddle oxfords) that will stop sickling?

Go to a podiatrist (foot doctor), and see what they say, but if your teacher is right, you will end up getting a pair of Orthotic insoles (or "Orthotics", as they are more commonly known) to wear in your every day shoes. They will correct your alignment and slowly over time force your body to correct its posture so that you stand and walk in the correct position. But be warned, they can be quite expensive as they are made specifically for your feet. Make sure you ask around and go to the right podiatrist when getting your orthotics made, because each doctor makes them differently and some are known for being better than others. It is also a slow correction process usually and is not a quick fix, but if you are willing to go through with it, it may be beneficial in the long term (this is all assuming your ballet teacher is right, but only a doctor can tell you if you need them or not).

Orthotics are very helpful for a lot of things, but I don't know if they will help your sickling as my feet natural sickle like you wouldn't believe and I have worn orthotics for 5 years and they still sickle. It's more about ankle strength and flexibility. My ankles aren't very strong and they are hyper flexible. They might help you, they might not.