Overwhelmed by the news

Nothing in the suttas asks anyone to stop caring about suffering far away. They do separate what arrives from what occupies the mind: gain and loss, pleasure and pain come to everyone, and the difference is whether they take up residence. The acrobats' simile answers the guilt about sitting — caring for yourself is a way of caring for others — and the boundless states are practices of care meant to reach everyone, including the people in the headlines. What the suttas do not supply is a news diet or a political program. If the dread is constant and is stopping you from sleeping or working, it is worth taking to a doctor as well as a teacher.

What the suttas say

So gain and loss, fame and disgrace, blame and praise, and pleasure and pain don’t occupy their mind. They don’t favor gain or oppose loss. They don’t favor fame or oppose disgrace. They don’t favor praise or oppose blame. They don’t favor pleasure or oppose pain.
The difference the Buddha draws between a well-taught noble disciple and an untaught ordinary person is not that praise and blame stop coming — both meet them — but that for the disciple they no longer take over the mind.
Where this stops: It describes a disciple who reflects that each condition is impermanent; it is a training, not a mood to put on after a bad review. Not a reply to bullying or harassment at work, and not a reason to say unfair criticism does not matter.
AN 8.6:6.1–6.5 · Worldly Conditions (2nd)
And how do you look after others by looking after yourself? By development, cultivation, and practice of meditation. And how do you look after yourself by looking after others? By acceptance, harmlessness, love, and sympathy.
The acrobats — the case that solitary practice is not selfish, and that care for others is itself practice.
Where this stops: For the worry that time given to one's own practice is taken from the people one cares for; not for a decision about having a child, and not a ruling on how to care for someone who is ill.
SN 47.19:3.1–3.5 · At Sedaka
Even as a mother would protect with her life her child, her only child, so too for all creatures unfold a boundless heart. With love for the whole world, unfold a boundless heart: above, below, all round, unconstricted, without enmity or foe. When standing, walking, sitting, or lying down while yet unweary, keep this ever in mind; for this, they say, is a divine meditation in this life.
The Metta Sutta's central image, in the canon's own words.
Where this stops: The verses are an ideal of the practitioner; the opening lines describing a skilled and honest person are a description, not a prerequisite for beginning. Never use it to quiet anger that has something to say, and never present it as a recitation that protects anyone. The mother guarding her only child is not for someone after a pregnancy loss.
Kp 9:7.1–9.4 · The Discourse on Love
Don’t run back to the past, don’t anticipate the future. What’s past is left behind, the future has not arrived; and any present phenomenon you clearly discern in every case. The unfaltering, the unshakable: having known that, foster it.
The Bhaddekaratta verses — letting go of the chase after what is gone and what has not yet come, in favour of what is here.
Where this stops: The verses go on to urge effort today, since no one knows whether death comes tomorrow; they are about where attention goes, not a dismissal of planning or of a past that still needs repair.
MN 131:3.1–3.8 · One Fine Night
As the wind cannot stir a solid mass of rock, so too blame and praise do not affect the wise.
The same teaching in four lines, short enough to carry into a meeting.
Where this stops: An image of the wise, not a demand to feel nothing when criticized.
Dhp 81:1–4 · 6. The Astute

Bring your own situation.