In regards to eating the blood of a fish, the Rambam in Mishnah Torah, Ma'achalos Asuros 6:1 writes:
אֲבָל דַּם דָּגִים וַחֲגָבִים וּשְׁקָצִים וּרְמָשִׂים וְדַם הָאָדָם אֵין חַיָּבִין עָלָיו מִשּׁוּם דָּם. לְפִיכָךְ דַּם דָּגִים וַחֲגָבִים טְהוֹרִים מֻתָּר לְאָכְלוֹ וַאֲפִלּוּ כְּנָסוֹ בִּכְלִי וְשָׁתָהוּ מֻתָּר.
But the blood of fish and grasshoppers, and shkatzim and ramasim and the blood of a human, one hasn't violated the prohibition of consuming blood. Thus the blood of the fish and tahor grasshoppers are permitted to eat, even if one gathered it into a vessel and drank it
The Shulchan Aruch (YD 66:9) codifies this but only allows it if a certain condition is met:
דם דגים אף על פי שהוא מותר אם קבצו בכלי אסור משום מראית עין לפיכך אם ניכר שהוא מדגים כגון שיש בו קשקשים מותר:
The blood of fish even though it is permitted if they are collected in a vessel is forbidden because of appearances, so if it is clear that it demonstrates such as having scales allowed
Bottom line: it's allowed provided you drink it with fins/ scales near it so there would be no issue of "maras ayin."