How can I get over my childhood trauma that affects me till this day?
There are numerous ways to get over childhood trauma that happened years ago. You can also gain information concerning your mother which may lead you to a family of half-siblings if she had other children. There are many reasons why a person does not raise their own child and most are not done with an intent to abandon or reject the child.
Concerning treatment, there are numerous methods of Cognitive Behavioral Therapy (CBT) available today and any one or a mixture of them may be instrumental in effectuating the change you are seeking. EMDR (Eye Movement Desensitization and Reprocessing) is a popular method of treatment and is known for effectuating change more quickly than any other method. It involves the use of bilateral stimulation to assist the brain in its focus on using the entire brain in treatment and it is available in many locations. I would recommend this method of treatment. EFT which is also called tapping is important in the field of trauma. It involves the meridian of the body (core) and frees electrical impulses which are stuck or which sometimes become stuck during treatment. The benefit with tapping is that it can be done in the clinician's location or done by the client in their home which makes it very private. There are numerous other methods all of which are capable of making change. Neurolinguistic Programming is useful and has been used for more than 20 years. Somatic methods are also useful and all of these may be mixed with various alternative methods of treatment. I think that you will be able to find a clinician at Better Help to provide your therapy.
Many people who were given up for adoption find that they are able to find half-siblings using ancestry.com to match their DNA with that in the database. Just as many people are able to make a connection with these family members that they never knew. I don't see where you mention what happened to your father after he was incarcerated. Was he ever released from the state prison? If so, you might find him or other family members you don't know.
With regard to the little child inside of you who you feel is crying out, it is possible to heal that child through the work of Charles Whitfield. Attachment work can also assist with the residual complications which grow out of your traumatic separation from your mother. In all likelihood, she felt that she could not manage to raise you and supporting you alone. I would encourage you to go forward with your recovery and search.