Disclaimer: The characters are borrowed and returned (hopefully) in mint condition. Not mine. And just to be safe I'm not making any money from this either. Just some speculation on what's going through the Doctor's head post-Doomsday. Thanks to Indemaat for beta-ing.
He always tells himself that the latest companion will be the last one. The pain is so great, all but swallowing his soul and he wonders if the reason Time Lords have two hearts is because they have more than their fair share of breakages. While it lasts companionship is wonderful but, as the Time Lord knows only too well, nothing lasts forever and the loss drains all of the joy out of life.
Now she's gone, nothing seems worth it anymore. The seventeen moons of Djhraxiraliad; the forests of the Elloan Federation of Independent States; the singing stones on Allushasinia, none of them are of any interest to him anymore. Not now he doesn't have Rose to share them with.
He would give anything, anything at all, to have her by his side and it hurts him so badly that he never got to say he loved her. Because he did. He loved her so much that he had burnt a sun just to say goodbye. And he would have done it again and again and again if he'd thought he could just tell her. But he can't. Because she's gone. Forever.
The pain never entirely leaves him; he remembers every one of his companions, his laugh, her smile, another one's energy and lastly and most prominently the look in Rose's eyes as she was torn away from him. That image hasn't left him for a second, like the unbearably bright lights etched onto the retina when it looks straight at the sun, and all he can do is blink back the tears and wait for it to fade.
Another second and he might have let go and followed her, even knowing where they were going and what it meant, because he loves her, like he loved and still does love all the others, with all his hearts. And there's always moments when he thinks he'd give anything to die with them and not have to bear the loss again.
He promises himself not to get entangled with life forms who burn so brightly with life and youth that he just knows they're going to fade and fizzle out and die and when they do the darkness they leave will be blinding.
But even as he does he knows from experience he's going to meet someone, somewhere and there'll be a glimpse of the last one in their smile or their scowl or their laugh and he'll let them get close to him. And later, when he realises that that smile, or scowl or laugh is not a substitute for the last one but something unique and special in it's own right he'll love them even more for it.
It feels like a betrayal to admit it but there is room in his hearts for Rose and all those before and after her and there will be another and another and another until he dies because the pain is hell but loneliness is worse than hell. And companionship is better than anything.