The gyro compass can drift more quickly if it is needing an overhaul or there are faults/wear etc. It shouldn't drift that much in 15 minutes and at all times should reflect smoothly any heading changes.
FWIW I have jotted down some suggestions if you want to get better at using the magnetic compass - use them if it helps, ignore them if not.
The magnetic compass can difficult to use if you aren't familiar with its foibles. If you develop an understanding of how it behaves and practice a bit you can become quite comfortable with it and that will give you confidence.
It is a fun exercise to get used to using the magnetic compass. Do it somewhere you are comfortable with the surroundings so you can find where you are (or grab an instructor). Then practice a series of turns onto headings using only the magnetic compass. Ignore the DI altogether for a while.
Firstly - it seems to turn the wrong way to most people. Try to think of the inside compass part (what turns - where the numbers are) as being fixed to the earth *not* the aircraft. When deciding if you need to turn left or right using the compass, think how you would turn the outside of the compass housing (the aircraft) around the inside markings to get the heading you want.
Secondly rather than rolling out on headings based on the compass reading, try and estimate where the roll out point will be before turning (ie pick a feature on the horizon), and roll out on that point and then correct once the compass stabilises.
So eg you are flying on a heading of 270° and decide to turn right to 020°. First estimate where on the horizon that heading will be (ie 110° to the right - a bit over 90°). Then turn onto that point. Once you have rolled out, check what the compass says once it is stable. Correct with gentle turns if necessary using the same technique.
Finally, did you learn the mnemonics for compass use in your training?
When getting a feel of the compass, when turning in the northern hemisphere++, use gentle bank angles and say "OSUN" (I need to Overshoot South and Undershoot North) when turning through northerly or southerly headings (ie the northerly heading readings take a while to appear on the compass so you should roll out before the compass says you have hit the right heading. After getting level it will catch up).
Similarly in the Northern hemisphere++ use "ANDS" for accelerating (eg when pitching down) and deaccelerating (eg pitching up), ie you will see the compass goes North when accelerating and South when deaccelerating - don't chase it, wait until you are not accelerating to get an accurate reading.
In turbulence the aircraft will be accelerating and deaccelerating all the time, and this will make compass use trickier - try and get an 'average' value rather of how it is moving.
Picking a reference point on the horizon first is a good technique even when relying on the DI for navigation and as a way to hold a heading without constantly staring at the instruments.
Like I said, just some suggestions, feel free to ignore.
++(In the southern hemisphere use ONUS and SAND)