Hi Ewan,
Hard to tell from your description alone (without any screenshots), but here are somethings you should check/do:
There might be so-called ‘double Vertices’ and/or inconsistent Normals.
Select everything (in Edit Mode) with A and then M > Merge >> By Distance, followed by SHIFT+N. (This is something you shoud=ld ‘always’ do, when things behave unexpectedly during Modeling.)
That might already fix it. If not, Make sure you’re Beveling the Edges and not the Vertices and look at the Profile Shape (maybe even the Type):