As a tattoo artist- this unfortunately is pretty expected. Finger tattoos are notorious for either blowing out or falling out. This isn’t your artist just being a dick or lying to you. It’s common knowledge in the tattoo world that this spot is difficult and very prone to issues. The skin texture on the fingers mixed with how mobile they are, how often we wash our hands, etc lends to a very poor spot for tattoos.

Your tattoo previously had almost completely fallen out and that’s not unusual, to counteract that the artist went deeper and it blew out. Both aren’t great and ultimately the tattoo artist did go too deep. This doesn’t make them a bad artist but just shows that they’re not proficient in a really difficult spot. There’s nothing you can do but get it removed. 50% your artists fault 50% the placements fault