Yes, Christians can seek counselling support for depression or anxiety. Pray to the Lord Jesus to direct to a professional Christian counsellor. The professional counsellor would be able to understand the root cause for depression and be able to help to deal with it. Anti depressant medication as prescribed by the doctor also would be able to help along with the counselling sessions.
Definitely seek medical advice from a Christian counsellor as God would be able to heal through the counsellor as well. Also seek prayer support from a Christian friend or Church group if you are comfortable to share that you are going through depression/anxiety.