Glad that you have got your admission pending the submission of the correct documents.
In CBSE, the procedure is standardized.
1. Download this application form, use separate ones for 10th and 12th.(http://www.cbse.nic.in/faq/MM%202016%20Duplicate%20Form.pdf). Please read page 4 of this pdf file, it mentions the charges for name correction Rs:1,000.00
2. Please read through the guidelines regarding the forms (http://www.cbse.nic.in/newsite/dup.html#guidelines), check the fees for name correction service, the delivery charges etc.
3. Choose an office close to you, in Delhi and apply for the 'URGENT BASIS". Here you have to submit the necessary documents, pay the higher fee for URGENT SERVICE and often you can get the documents in two working days.
So, please gather all the evidence,
your present certificates
proof of father's correct name, spelling, and initials
rest of your school documents.
If you have any doubts, then meet the administrative office of your 10th and 12th schools, the officers/staff will be able to help you.
Since time is short, I would also suggest having a correct name affidavit made for your father. This can be done once you meet the Notary in your local civil courts/offices, this would be legal proof of your father's correct name. This can be done on the same day. By evening, you can publish both in local newspapers (English and Vernacular), then you would have all the documents in hand.
Please also use this opportunity to check your other documents PAN,Aadhaar,Voter's, Driving License,caste certificate if any.