Distinguish which alert was triggered

We have integrated Sentry with DataDog, and have an “alert” set up in order to be able to send the events over to DataDog via the integration (The alert is “An event is seen” sends to Webhooks at most every 5 min - the most frequent possible.)

However, we also want to be able to alert when there is a large volume of events coming through, using an alert in Sentry which would send to DataDog, and then DataDog would alert the team via an OpsGenie integration.

As far as I can see though, there would be no way to distinguish the Sentry alert that is just sending the regular event stream to DataDog from the alert that is being set off because there are more than X events per Y minutes.

(1) Is there a way to add a tag, alert title, or other such information to an alert that is sent out via integration, so that they can be acted upon differently in DataDog?

Also, (2) since alerts are only sent out when a new issue is seen, according to the docs, would that mean that if an existing issue that only had a few events started having a very large volume of events, that there would be no way to alert based on that?