Does Islam obligate us to give Daawa to every person we know? Or does it say that at the end what really counts is the good deeds you did towards the people?
This is what the Qur'an says about Daawah.
By time, Indeed, mankind is in loss, Except for those who have believed and done righteous deeds and advised each other to truth and advised each other to patience. (Qur'an 103)
The main purpose of Daawah is that when a person is facing a hard time and he might be going in the wrong direction, then his fellow believer could help him out and show him the right path. Again when this second person if at all gets misguided, then the first person could help him out pulling him out of Darkness. Today Daawah might have got moulded into different meaning.
does it say that at the end what really counts is the good deeds you did towards the people?
Yes, of course. In the end, what really matters is the good deeds.
But Islam gives you a shortcut to stay on the straight path and do good deeds.
May the creator guide us all.