Eventually, the rain will stop and you can find a roofer to fix the leak (no rush – because roofers are always busy after it stops raining)).
You can try the SES – but they will take a while to get to you and if they throw a tarpaulin over your roof – they can cause more damage to your roof.
The reason people stress out when the ceiling is leaking is just the thought of the damage. If you can just let the rainwater pass through the ceiling and have a container to catch it under the ceiling – then there will be a minimum of damage.
Just go with the flow – not against it.
For further ease of mind, there is a roof repairs checklist for homeowners that you can check out to see if you have covered everything…