How can I handle depictions of suffering better emotionally?

My problem used to be a bit different, but maybe my tips from Dissociation for Altruists are still helpful for you!

Some people do not lack in altruism and are well aware of effectiveness considerations too, but the sheer magnitude of suffering that effective interventions would force them to face is too unbearable for them to acknowledge. I give tips on how they can use dissociation to put altruism on a more scalable basis.

This, for me, is why I mainly engage with simple rules (give 10% of income through payroll giving to Givewell recommended charities, don't eat meat) and only occasionally do deep dives into the fundamental philosophy or actual individual suffering. 

I don't so much disengage as just get really sad, which on the one hand, yes, the world has a ton of suffering in it, but also it's hard to operate with that level of sadness constantly. The engagement/reading for me is more like a 'sadness top-up' once in a while to make sure I stick to my rules.   

I'm currently researching the related topic of the compassion-oriented Buddhist spiritual path, so my response will be from that perspective. Feel free to DM me if you want to chat. 

John Makransky, of Boston College and Kathmandu University, has done great work on this question. He adapts Tibetan Buddhist practices for a secular Western context. See "Compassion Without Fatigue: Contemplative Training for People who Serve Others" (third link from the top). The main insight for me is that I am not alone in trying to alleviate suffering--so many people throughout history have stood in compassionate solidarity, and I can draw on them for support.

Makransky takes the opposite approach of commenter Denis Drescher--he (and the Buddhist tradition) believe that reducing feelings of compassion is not the answer. Boundless compassion (along with boundless wisdom) is quite literally the goal of the Mahayana Buddhist path, so it's wonderful that you feel so much compassion already. Countless Asian philosophers have been developing these ideas for millennia, so they've inevitably come up with some good ideas and coping mechanisms!

For a beginner-friendly philosophical analysis of the progression from painful compassion to wise equanimity, see Sadness, Love, Openness by Chökyi Nyima Rinpoche. Note that this author is a Tibetan lama, so he takes a more religious approach than Makransky.

Hope this helps!

I can’t look inside your head, but if the mere thought of something makes you suffer, it probably means it reminds you of something that you are trying to ignore, i.e. trauma.

Assuming that this is indeed the case, I would further speculate that you are ignoring this memory or unpalatable insight because you subconsciously expect that thinking of it would disturb you to the point of getting in the way of whatever you would prefer to be doing, like idk, whatever your daily pursuits are.

The solution then, given these assumptions, would be to set aside some time (a week or two) to sit on a pillow and have nothing to do. This tends to bring unresolved trauma to the forefront by itself, simply because there is finally space for it.

Unfortunately you always find that there is more stuff to deal with, so this kind of spiritual work is a lifelong process (of getting progressively happier). I wholeheartedly recommend it.

Protect yourself!