Saying goodbye is never an easy thing, even if you did say forever. The Doctor knows this; he has been there so many times. Staying in Pete’s World with Rose had been a no brainer. Only one could stay with her, or take her and he had been the chosen one. For the last 40 years he and Rose had done so much. Worked at torchwood, grew a TARDIS and traveled the stars. They had learned so much too; Rose didn’t age, at least not much in the last 40 years, she maybe looked 23. He hadn’t aged in that sense either, still looking like the day that he was born from the hand. He was Rose’s Doctor and at first had always assumed that he won and this was always how it would be.
He knew that if the other, “original” him had known about Rose he wouldn’t be here now, she would be safe in the right universe, with a man who would live a long time, not one that had been slowly dying. During the first few years in Pete’s World they had been so busy neither of them had noticed. They had Mum, Pete, and Tony. They had jobs, then the TARDIS. He slowly noticed about five years in that he needed more sleep than normal. He put it off as just another human condition he had to deal with, and then the pain came. He had hid it from Rose; he couldn’t tell her that the medicrisis didn’t work right, that there forever was short. He did tell her she wouldn’t age and that he should live as long as her, but that was before.
Once the Doctor had realized the truth he started to make a plan to keep Rose safe and save her from a horrible painful end of her life. He had always known that she loved them both; him and the original, neither of them could have ever made her chose between them. He kept his pain and the fact he was dying hidden from Rose, he had promised never to leave her and he wanted her happy, so he would wait tell the time was right to tell her and let her go. He kept his pain at bay with the help of his Time Lord biology that helped with pain control. When it got worse the TARDIS and pain medications would help, most the time. If Rose ever asked it was normal, just a human thing.
By year 15 in Pete’s world Rose started to get severe migraines. They could be usually dealt with without pain medication and the Doctor at first had assumed that it was part of the Bad Wolf that had changed her. After some testing on the TARDIS he realized that it was the universe, it had never actually compensated for Rose being there, over time it was going to kill her, though she would live a lot longer than him and not really be safe after he was gone. He decided to keep watch on the progress of his decline and Rose. He would need quite a while, even with the help of the TARDIS to calculate getting himself a message, getting the correct calculation on a transdimensional hole, and when exactly to get the message to the right Doctor. The worst and hardest thing for him was to figure out how and when to tell Rose. So he did what he normally did and he ran as fast and far as he could, for as long as he could.
In their first year they had many ups and downs. She had worried a lot that he would leave her; he felt sometimes that he was fighting a ghost, the ghost called his other self. The second year they had married, with Jackie and her big wedding. They worked for Torchwood and got a flat of their own. Her mother started pushing for children. The Doctor couldn’t give Rose that, even if he wanted to. Rose was quite happy with their life and the fact they were growing their own TARDIS and didn’t want children, she wanted it to be Rose and the Doctor in the TARDIS as it should be. By year 4 the TARDIS was ready to fly and off they went, learning about their new universe. They ran hand in hand through the galaxies getting in trouble, the bits in between.
It was during the traveling that the Doctor had noticed the pain and needing more sleep. He put off finding out what it really was, he didn’t want to know. He did realize that Rose was not aging around the same time. Though he put off telling her about himself he told her about her changes. When he had learned about him and the originals mistake in thinking that nothing had happened with Bad Wolf he had been angry at both him and his other self. He took Rose’s hand and they ran. They ran from the truth until Rose started getting more and more headaches. They were easily controlled with medication for many years and the Doctor thought it was part of Bad Wolf and aging, another mistake he made, because he liked to run from the truth.
When he had finally tested Rose after an accident, he then knew that she was slowly, very slowly dying. She would die because of this universe. He would save her at the cost of his heart, but he would not be living long after she left. One she would take his one heart with her, she was his reason for existing and living. Once she was gone, he wouldn’t want to live. At the rate of his cellular degeneration he would be dead in just a few weeks maybe a month or two with the help of the TARDIS.