How can I face my depression & anxiety, and try to get back to normal?

A termination in this context would be a traumatic experience for most women. It has been compounded by the background you describe as I suspect you did not have support from other family members either as you went through a very difficult and conflicted decision. This can make it even harder to move on from. I recommend you seek professional help to work through the many emotions you have associated with this situation and your relationship with your father.  
 
In my experience, the most effective type of therapy to help you rapidly resolve your feelings would be EMDR (Eye Movement Desensitization & Reprocessing) Therapy. This therapy is one of two therapies identified by the Australian Centre for Posttraumatic Mental Health as being an effective treatment for PTSD (Post Traumatic Stress Disorder). I have now practised EMDR for the last 19 years and also found it to be a highly effective and rapid way of resolving grief and childhood abuse.
 
I suspect your situation would have components of both grief and trauma in it. EMDR goes beyond “just talking about the trauma” as much of your experience of trauma and grief cannot be put into words. Also, the research shows that just talking about it can make things worse as it gets you in touch with painful emotions but does not help you process them at an emotional level. This is the real power of EMDR. It allows you to finally put the trauma behind you and move on with your life and an be happy again. For more information on EMDR and a list of EMDR practitioners in your area, see this website http://www.emdrtherapistnetwork.com/.

I am sorry to hear that you had to have a forceful abortion. I know it is hard. I had an abortion myself. I have chosen to have it, but it was hard and still hard. I was feeling sad after the procedure and cried frequently. I also counted days of a due date of a baby who would have never be born. It is hard, but I could move on from that traumatic experience. I had a great family support, which helped tremendously. If your family is not supportive, I recommend you to have counseling. Just please do not blame yourself. You did the best you could. Now it is time to heal and try to move on. 

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Wow, you are so hard on yourself - even beginning your question by asking readers not to judge! It sounds like you judge yourself very harshly for the way you have responded to difficult circumstances. 
Judging ourselves harshly when we feel powerless and overwhelmed is a common coping strategy. It can give us the feeling of being in control - it goes something like: “If I judge myself, then I can change myself and feel better”. However, where we are in situations where we have limited or no influence over what other people choose to do (such as being a child in a family where a parent is violent) this way of thinking can keep us stuck and miserable.
It may not seem intuitive, but being kind to yourself - forgiving yourself for not being able to cope better, and acknowledging that you did the best you could - is a strategy that will ultimately  give you more control in your life, even if taking that control means walking away from family members who either will not or cannot acknowledge the impact of their behavior and choices.
Working on changing your relationship with yourself - between the part that feels overwhelmed and the part that judges - may be an important thing to do. Counselling can assist you with this - you may need someone there to support and champion the more vulnerable parts of you, to help them realize they are worthwhile and lovable, just as they are.

It is great that you have a desire to get back to the happy and bubbly person you were. As has already been suggested, it would be really helpful for you to have some counselling to assist with this process. It sounds like you have had a very rocky journey with your family history and the abortion and the coercion. The good news though is that therapy will make a difference to all of this, and, as you already have an experience of yourself as happy and bubbly, you will be able to build on this to develop compassion and acceptance for your experience and circumtances. It is not surprising to hear that you have been diagnosed with depression and anxiety given what you describe. Forgiveness is possible though with the right help and support. Family history does play a very significant part in your diagnosis. Healing will come as you embark with courage on this process. All the best, Margie