Having worked in healthcare, I know what you mean. You develop a thick skin and a non reactive attitude so you can cope with extreme levels of stress without breaking.

Developing compassion can be done in many ways. The Dalai Lama has a non-religious approach to compassion. You can find ways yourself to care for others.

Here are some articles that may be provide some insights on compassion
Psych Central - Search results for Developing compassion

Don't be so hard on yourself. You are wonderful.