Can a new mother have post-partum depression even if she was a surrogate and the child is not biologically hers?

Yes. The surrogate still went through the process of pregnancy and the hormone and bodily changes involved. If there was also a history of depression in the surrogate or in the surrogate's family, the risk is there.
If you need PPD. Support. Reach out to a psychologist for an assessment and individualized treatment. Consult w/ psychiatrist regarding med options. Explore group therapy or meet ups. This can be in a formal setting like a postpartum support group or a less formal surrogate support meet up. One of the goals is to increase your support network and avoid taking on PPD alone.