My 4 month old woke up this morning with a blood spot in her eye close to her inner eye. Is it normal and what maybe causing it?

Eye blood clot. Small hemorrhage sin the white part of the eye can happen due to several causes. Extreme coughing or vomiting can cause it, as can coming through the birth canal. It is less common for it to happen spontaneously but if bleeding is only in that area and nowhere else it should resolve itself within a week or so.