I'm sort of late to this thread, but I feel compelled to express my condolences to you and your family. I have three dogs myself and I think everyone here will agree that pets - especially dogs - are not just pets. They are family and one of the few other animals we encounter that will give you unconditional love. Being in the medical profession myself I understand when you say it's strange being around illness and death regularly. It's "easy" to make it purely clinical and distance yourself emotionally but when it's family we can't do that.
Just remember all the others you do still have around that you love and who love you. The sharpness your grief will ease with time. My best advice (not that you need it or asked for it) would be to remember and cherish the fun and happiness your pup gave you. It may sound peculiar talking about the grief process this much but, this is what we do for family.
We're all here for ya bud...hang in there