HI
1) Since your birth certificate carries the name of Anam Amrin and holds a date of birth of 21 Jan 1989, you can use the same to have all of your school certificate, PAN , Aadhar corrected to reflected as 21 Jan 1989.
2) It appears to be a typographical error which was not noticed by your school teacher's and parents and you can claim typographical error as rationale for the inadvertent error to creep in
3) You should
a) prepare an affidavit stating your date of birth as 21 Jan 1989,
b) Publish the date change requested in 1 english and 1 vernacular news paper,
c)Submit affidavit, news paper publications and Attested Birth certificate reflecting the DOB as 21 Jan 1989 to General administration department, Secretariat and
d) If all papers are in order, the GAD department will have the DOB and amendment there of published in the gazette thereafter.
4) Subsequent to publishing the gazette notification, Making changes to Date of birth will require you to apply to make separate applications to universities and authorities (X,Inter, University, Pan card, Aadhar and passport) by submitting
a) copies of birth certificate attested by a Gazetted officer,
b) copies of gazette published and get your date of birth corrected in all your records.
5) Unfortunately unlike name change which is a 3 step process, the date of birth correction in all of the academic and statutory records should be done for each certificate individually and is time consuming and will take about 30-45 days for publication in gazette and another 3 to 5 months thereafter for having the correct date of birth mentioned in all of your marks cards, Pan card and aadhar card.
Hope this information is useful