Does this sentence only focus on the blood quality or could i mean "I'm from a good (noble) family"?
If I had to guess,I've seen a couple of like phrases before. Blood, seems to me, to be culturally associated with the quality and strength of one's character, or "breeding". If only metaphorically. The way a surname can be in English.
Because the sentence is not focused on the existence of the blood, only on it's quality. It's already assumed that the person speaking does indeed have blood, and the only new information is that the blood is good.
Why not «моя кровь хорошо?» or something similar? I suppose the question is why use «у [genitive]» instead of a posessive?
Because the sentence is saying I have good blood. The есть is optional, and sounds more natural without it.
If the sentence was моя кровь хорошая then it would be "my blood is good" which while synonymous isn't the same sentence as "I have good blood".
Кровь is also a feminine noun, just as an aside.