*URGENT* Need advice on Re-applying Tier 2 General Visa

[wenwi1234]

Hi guys, I will need some urgent help on Tier 2 Visa.

I am a secondary school teacher but I am moving to a new school to teach this new academic year, and at the moment I am currently holding a Tier 2 - leave to remain visa for an year which expires on the 14th September 2018. however, I thought I had to leave the country and reapply for a new Tier 2 Visa, but the visa was refused on the 16th August (submitted the biometric data on the 2nf August 2018), didn’t received my passport back till the 7th September 2018. The refusal reason for my application was the cos that I have provided does not fit the category that I am applying for. I had a check the COS that the school provided was a Tier 2 General - Switching Immagration Category. I have currently booked my flight back to UK on the 11th September.

Now I have re- applied Tier 2 leave to remain from inside the UK using the premium service yesterday on the 9th September but the appointment time for the earliest interview is on the 21st September 2018, my current visa expires on the 14th September 2018 and the COS that were issued by the school will expire on the 15th September 2018.

Question 1: Am I applying the right category?
Question 2: will I need to ask my school to reprovide a COS? Or I can still use my COS? Can the COS be changed or extended as the COS provided in the application is expired?
Question 3: As my visa expires on the 15th September, would I become an overstay?
Question 4: any suggestions that I need to do further ?

Really need some URGENT help

Thank You