Are these OK?
(injury etc.)
It's nothing in comparison with mine. / It's no big deal in comparison with mine.

No matter what the situation is, we should never give up.
No matter what the situation is, we should never despair.

(It was a tiring day)
I slumped into the chair from exhaustion as soon as I came in. (into the house)

Question

Are these OK?
(injury etc.)
It's nothing in comparison with mine. /  It's no big deal in comparison with mine.

No matter what the situation is, we should never give up.
No matter what the situation is, we should never despair.

(It was a tiring day)
I slumped into the chair from exhaustion as soon as I came in. (into the house)

Answer

Yes, all the example sentences you wrote are OK.

And you could also use another phrasal verb. For example,

"No matter what the situation is, we should soldier on."

"soldier on" to continue doing something although it is difficult: I admired the way she soldiered on when her business ran into trouble.

Answer

Yeah good work