Can I claim my brother as a dependent and get ctc and eic?

You need to know that neither parent claimed him, and he had to have lived with you, and had no income. (If he had a small income, answer below.)
You can file an amended return.
You could have checked to see if you were entitled to the EIC without a dependent. I don't know why so many people seem to think you have to have one.

Forgot that to be 'child' he must be under 19 on 12/31/10 or under 24 if a full time student.

If under 17, you can claim the child tax credit. You can use 1040A form, not EZ.

Your brother would have to agree to file an amended return in which he indicates that he is a dependent of someone else. This is likely to reduce his refund amount, and if he has already received a refund he will likely have to pay some back to the IRS.

He is 19 now and a full time student

Thank you your answers were very helpful