An aircraft may balloon with the application of flaps, as it may settle with the retraction of flaps - if the pilot is inattentive to flying the plane, and fails to manage speed and pitch. Otherwise, things should be fine. The first extension of flap will nearly always result in an increase in lift - different amounts for different aircraft type and flap configurations. So, yes, if you add lift, without compensating in another way, the plane is going to go up! Similarly retracting flaps when the aircraft configuration is not optimum - it's going to go down.
As Englishal has said, most every plane I have flown will require a nose down control input to maintain path, with flap extension. I seem to recall the C 310 and DC-3 less so, as they have split flaps, which contribute more to drag than lift.
So, as the pilot new to the type, you can allow yourself one excursion from your intended path while you understand how much nose down control should be anticipated with the application of flaps in that type - after than, you're responsible for applying your skill to anticipating the affect, and applying control to result in a smooth flight.
Piper Cherokees have delightful manual flaps, which are moderately effective through their range. But, you can apply them all at once, if you choose to. Most Cessnas have really effective flaps which are electric, so it's really the speed of the flap motor which governs the pitch change associated with flap application. However, much older Cessnas and all 180/185s have manual selection of those same flaps, so you can get all of it at once - you've got to be ready for that!
Contrary to the practices of others, I do not reduce away from use of full flaps for GA aircraft I fly)* exception once). If a Flight Manual presented a limitation to this affect, I would follow it, but I've never seen one. The crosswind capability of the aircraft was demonstrated with full flaps. With full flaps, you're going more slowly. Were something bad to happen on the surface, going more slowly is better. Slowing the aircraft on the surface with greater aerodynamic effect saves tires and brakes.
*The exception was when I was flight testing the first Z701 with a test pilot friend. It had an abomination of flaperon, the result of which was that as flap was applied, aileron travel was used up, so at a slower speed, you had less roll control available. That is the reverse of what was needed. I did have to use less than full flap for some crosswind landings in that. I commented this back to Chris Heinz. I'm confident that was resolved somehow, though I have not flown a 701 since, so I do not know.
The wheelbarrowed landings I have witnessed on Twin Otters were unintentional and bad! We don't do that! When I was trained in Twin Otters, I was limited to 20 flap, until I demonstrated that I had the skill and feel for the plane to maintain good pitch control with full flaps.