Shared neutral on the same leg
Absolutely right, this is super bad for exactly the reason you say!  Turn off both circuits and get yourself a 2-pole breaker of that same type.  Put the two hots on that breaker and install it, moving other breakers as needed.

The use of a 2-pole breaker will guarantee they are correctly on opposite poles, and is now required by Code.  (well, handle ties are, but it works out the same. 30 places near hear stock 2-pole breakers, only 1 stocks handle ties.)

Be careful not to split up another multi-wire branch circuit.   In fact, watch for more - where there's one, there's five. 

Also, make sure you're not dealing with double-stuff or the GE Q-line "half width breakers". In a Q-line, an intermediate breaker would be correct, but a 2-pole breaker would be a great deal more correct.