Looking for Half Sister?

What information do you have from your father? Is your half sister through your father's first marriage? If so, where is the mother? You should try to gather all the information you can from either of these people or from any close or distant relative as you will probably need more real facts to be able to find your sister.

Also, I do not know how large a city Chapeltown is but it seems that would be a good place to start. How do you know she was fostered? Can you inquire in any government office that may have some (even older) information on the foster family? Do you know anything about the neighborhood they lived in? Maybe you could take the photograph you have and just start showing it around and asking questions.
Finding someone through the social media does sometimes bring results but it may take years and may never happen.
It will take a lot of your time and leg work to get information but this may be the only way to find your sister.