Is there a phrase like 'in my joy'? What about 'feel the hours passing by'? [closed]

Are the phrases in bold in the following sentence correct? "In their joy of finding a friend in each other, they did not feel the hours passing by."

I'm not a native speaker. I feel like the first phrase needs to be reworded entirely. As for the second, I think I've read similar phrases in a number of books, but I can't find anything like that in a Google search. Maybe 'by' needs to be omitted. Also I get that 'lost track of time' can mean the same thing, but I want to convey the specific meaning of individual hours passing.

The phrases are correct. It's completely normal to use 'in' like this in normal speech or writing. It is not confined to creative or special situations. We can use 'in' about an emotion when we are discussing a thought or action, or omitted action, that was caused by the emotion.

In my excitement at seeing John, I let out a cry.

In his alarm because of the fire, he forgot that he was naked, and rushed outside.

In their pleasure at hearing the music, they did not notice that their dog was missing.

In my haste to complete the task, I forgot to sign the letter.

Also, we can omit 'by' after 'passing' when talking about the passage of time .