I hope you find a way to remain in touch with patients and their joys and tragedies, whilst tending to your own wellbeing. Making sure to know your emotions and what you can do to replenish your own reserves, and put in boundaries so that you don't burn out.
But i'd really caution against this idea that you are somehow not as competent, strong as others, or that you need to imitate the coldly detached attitude which is becoming standard throughout so many parts of the NHS.
Compassion fatigue is a massive issue in the NHS, partly due to the pressures and unkindness that is shown to staff themselves (which is horrendous), and partly in some places, it appears to be encouraged as an appropriate way to behave (which is truly awful and also dangerous, not to mention unpleasant).
Thick skins of the sort that may have once been a protective mechanism, but have become so hard nothing and no one can ever move them... Or in fact be identified as anything other than an annoying and unwanted task in the way of whatever that person really wants to do (like go home, have a tea break, fill in paperwork, etc etc). That level of objectification becomes a liability and as a barrier to being able to do a good job. If it stops people from being able to relate to their fellow human beings, then the way is open for accepting fellow HCPs cruelty, and beyond.
I think it's ok to let patients situations touch you, as long as you have a way of making sure it doesn't break you, or dominate your live.
For me, it's when HCPs stand by and watch shockingly bad 'treatment' (or lack of), inhumanity and abusiveness with complete detachment, that's when there is a problem. And for those people, who walk around oblivious of others pain and suffering, even when it's in their power to stop it, those are the people who have ended up letting their attitude have the most (negative) effect on their inner selves.
Even as they pretend that it's 'professional' or even just 'normal', they are harming themselves so much more than the person who is strong enough to see patients as actual thinking, feeling human beings, and can deal with that, the sad endings as well as the happy ones... Those are the people are both amazingly strong and deserve respect and who are amazingly good at their jobs.