You do not need to worry and remove thoughts about extreme steps for such simple mistakes.
If you have a valid caste certificate that says you belong to Schedule caste, you can change it.
I hope you and your parents would have mentioned about the scheduled caste status at the time of admission in the school/enrollment for 10th standard.
First, please have a valid caste certificate for yourself, your parents and your siblings if any. There should not be any doubt in this regard.
Then, please visit the CBSE school where you studied your 10th and 12th. If the admission register and details reflect, that 'as per the school records, Mr/Ms X belongs to the scheduled caste', it would be useful for your case. Please take a letter from the school principal stating the same.
You can also get an affidavit from a Notary, stating your caste by birth.
Then draft a letter to the appropriate CBSE authorities based on your region/state (http://cbse.nic.in/newsite/contact.html#reg).
Filling in a correction form one each for 10th and 12th, explain in your covering letter that, by mistake, you have entered general category during registration for 10th. Provide evidence of the above, school caste entry letter, copies of your caste certificate (and parents), affidavit and the fees.
Please keep all correspondence with the board handy for future use.
You can approach the school administration staff and principal for guidance. If the board does not issue you new corrected certificates, then you can contact a good civil lawyer who can help you get this correction done.