You really don't need one for biomath. For metric spaces, something like Searcoid's book, supplemented by Munkres' Topology for anything not in Seacoid / for a more abstract viewpoint.
For Galois theory maybe Stewart's book is a good choice. If you want something broader/higher level you can try M.Artin's or Hungerford's or Lang's Algebra, and just check out the Galois theory part (these three books being listed in increasing order of difficulty imo). Things will be terser in those books than in Stewart though.
My recommendations aren't really suitable to find honours stuff in though, they are more about expanding your toolkit.
You generally want to look at graduate level books/papers for honours projects, and talk to potential supervisors.