So I'm by no means an expert but here's what I would do:
It sound like you want to make the arrows actors right? you could also make them regions and do stuff basically the same way. Anyway assuming you are using actors for the arrows...
I'd work in the scene events and use an always loop. Then within that I'd have a conditional statement saying "IF mouse is pressed on {up arrow} set {y} speed of {actor plane} to some number... OTHERWISE IF mouse is pressed on {down arrow} set {y} speed of {actor plane} to some number...OTHERWISE set {y} speed of {actor plane} to zero
This works because you will only ever be clicking on one arrow at a time. first the program checks if you are clicking on the up arrow if you are it starts moving the plane up, if you aren't it checks if you are clicking down, if you aren't clicking anything it sets the up down movement to zero. preventing it from floating away.

If you are going for a more flappy bird style I'd take out the last bit of setting it to zero and just let the plane drift. Alternatively you could say "push {actor plane} in some direction" and then have linear damping in physics so it slows down
Hopefully this works for you!