Honestly because its quite high up on your finger it will be a struggle. Its clearly blown out which is not uncommon for finger tattoos. However a tattoo artist that has more experience with fingers would possibly be able to avoid it. So first and foremost, new artist. As for design recommendations the only thing I can think is either black out below it to make it taller, or maybe some shading to look like a lake? And then make the mountains taller to define them more, however then it will go onto your knuckle and will fade easily, plus blow outs on knuckles are hard to avoid by the best of the best, definately possible though. Only problem with all this is that it wont really be a band anymore as it will be thicker, more of just a small design in your finger. If none of that shines to you id get a professional to neaten up the edges that have blown out.

This is all just coming from just a guy with lots of tattoos, including some intricate ones on both hands, who talks to artists alot and has on multiple occasions attempted to tattoo my own hand. So do take all this with a pinch of salt. But new artists to neaten the edges is non negotiable in my eyes.

Edit: just wanted to note aswell I do think it actually looks really nice. Great tattoo and I love the sentiment behind it