I'd suggest you look at it as two separate actions:
- Can I add regression bugs to the product backlog so I don't lose track of them.
- Can I bring them into the sprint.
For the first one, I see no reason not to. I think Jira has a "bug" issue type by default and these are perfectly valid items to have in your backlog. If you want something more specific, you can always create a new issue type specifically for this kind of bug.
As for bringing it into the sprint, this should normally be a conversation between the product owner and team. Most mature Scrum Teams have an overarching sprint goal like "Users will be able to pull a report of their data usage over the past 6 months" and the team can speak to if pulling in the bug puts the goal at risk while the product owner can speak to the relative priority of the bug. Even if your team isn't quite to the point of having these clean goals to talk around, they can speak to what work might not get done if they bring the bug in.
The Scrum Guide states that during the sprint "No changes are made that would endanger the Sprint Goal". Many people take this further and say that no work should be introduced at all. That's not strictly true. In fact, the Scrum Guide also says: "Scope may be clarified and re-negotiated between the Product Owner and Development Team as more is learned." However, if your team is completely new to Scrum or not yet disciplined in managing incoming work, it may be safer to say that all those bugs wait until the next sprint.