It could be because you have a deep rejection of Dukkha You cannot develop Compassion if you reject Dukkha. This will only bring depression, aversion, fear and worry.
By actually seeing that we have aversion, fear and worry when we reflect on the Dukkha of others, we start to see our strong attachment to our ideas that we wish the world to be a happy place and that Dukkha did not exist. So if you are having depression, aversion, fear and worry, you are probably rejecting Dukkha. And also, you are not understanding the opportunity of opening to Dukkha with Compassion. Because Compassion is not a response to pleasure, it is a response to Dukkha.
It may be that you are trying to protect the mind, afraid that with too much awareness of Dukkha, you are going to get overwhelmed. But if you expand the capacity of your heart, Dukkha does not overwhelm you because you also understand there is a way out of Dukkha. If you are becoming overwhelmed, I would suggest that you reflect more on the Third and the Fourth Noble Truth. Not only seeing Dukkha, but also the way out of Dukkha. It is not by rejecting Dukkha that we find the way out of Dukkha, it is when we open to Dukkha, see it within ourselves and others and open with Compassion to it.
In particular, if you are falling into grief then you may have a limited idea of your capacity. In this case, I would suggest that you reflect on the Buddha, so that you understand the human potential more deeply.
It is not easy to open to Dukkha. But it is not easy to run away from it, either. The more we run away, the more we hurt ourselves. By learning how to turn around and expand the capacities of our heart, we realize that we have the power to make our mind bigger and open to it.