High Notes?

I'm not an expert so I don't know the exact terminology here, but bear with me.

I enjoy singing, and generally I can do high notes pretty well (albeit still needing a lot of practice, obviously). However, that goes mainly for males (and maybe a very few females), generally for females I find the high notes challenging to do. I'm a female myself, my voice though is not high pitched, I'd say it's more 'average' to deep. So, when I attempt female high notes, other than a very few exceptions, my voice comes out mainly squeaky? And I hate that.

Is it just a problem with my voice that I can't fix due to how deep it is, or can I somehow improve that? Any advice is appreciated!