Now that you have identified both breakers, remove the panel cover (if you are comfortable doing that) and follow the hot wires from the two breakers. See if they converge onto the same cable. Typically one will be red and the other black.
If they do, then you have an intended thing called a Multi-wire Branch Circuit or MWBC. You are almost OK, but there's one more thing to check.
Current Code requires that these two breakers have common maintenance shutoff so if you shut off one, the other must shut off. I hardly need to explain why, eh?
There's one more rule that has always been absolutely essential. The two breakers must be on opposite poles of the panel, so that there is 240V between them. If they weren't, the neutral wire would overload!
Wouldn't it be great if there was one breaker type that guaranteed both this and common maintenance shutoff?
There is. It is called a double-pole or 240V breaker. It resembles a dual breaker, except its handles are factory tied, and it fits in a double breaker space. Use the amp rating of the existing breaker, but no more than 15A for #14 wire or #12 aluminum, 20A for #12 copper or #10 aluminum.
Where there's one, there,s two. Search the panel for every such case of a 3-wire cable going to 2 separate breakers, and do the same thing with them too.
Otherwise it's a big mess
Other than the situation above, neutrals must only interact with their own circuit. Unfortunately, some electrical workers believe "If it works, it's safe".
One helpful rule here is that "currents must be equal in every cable or conduit", meaning any power that comes out on a cable's "hot" must go back on that same cable's neutral or some other wire in that cable. And that means wiring must be done in a physical "tree" layout -- branches can come out of the panel, but they can't cross-connect to each other because that would be a "loop" and real trees don't do that.
By the way, ground wires are allowed to loop / cross-connect, and should. That is because ground does not flow any power except during an emergency. This confuses people who already think ground and neutral are the same thing. They're not. Not even close.
The #1 place this kind of cross-connection shows up is in switch boxes with more than one switch. However, this one isn't any smart switch! You would not notice the tiny trickle from a smart switch, still, Do not allow them to poach neutral from other circuits. This can get tricky where 3-way switch circuits are smarted.