Urgent question about switching from tier 4 to tier 2

[Lizzo13]

Hello,

I have received a conditional job offer as a social worker and am in the final stages of having everything necessary to make it an unconditional offer. The problem is that my tier 4 visa expires on the 22nd October (2 weeks). I have background checks from other countries I lived in from 2 years ago. I was told that because I am applying from the UK and have been here 2 years already, I do not need the background checks to apply for my tier 2 visa. Is this correct?

Also, the employer has not given me the certificate of sponsorship number yet. I'm not sure where they are with it or if they've even applied for it. How long does it take for them to get it? I am in an absolute panic about this whole process, and HR haven't been very helpful. Thank you!