at one/some point

Hi, friends.
I have gone through threads about ‘at one/some point’.
But there is still something I am not so sure about.
Please look at the sentences that I came up with:

I went hiking today. It was really hot that at one point I felt like I was dying.

Here, to me, ‘at one point’ just emphasizes that the fact ‘ I felt like I was dying’ happened.
Do you agree?

If I changed ‘at one point’ to ‘at some point’, I couldn’t really understand it.
I seem to sense a difference between it and ‘at one point’.
But I am just not able to really explain it.
Please help.