Stick with it, its great being a Southpaw, its big advantage when it comes to fighting/sparring but you are right can be a pain when training with a partner in a class situation as you will often be shown things that won't work from your stance. It could be a good idea to discuss this with you coach.
If something isn't working for you, you could try and adapt it, try stepping at a different angle etc, switch part way through or whatever (switch hitting can be a usefull thing to learn). Or ask your coach for an alternative techniques. Myself I ended up often changing the drills to ones that came more naturally (obviously be sensitive to what you coach thinks about this, it could come across as arogant if you just start doing your own thing i.e - you think you know better!). Or as H1SSY suggested just switch, not the most satisfactory answer but sometimes its the least frustating option.
Obviously you will develope your own style over time but I have found the following usefull:
For sparring the standard advice is to rotate right keeping yourself away from their cross. Keep your right foot to the right of their lead foot. If your in that position your in a much better position to attack & they are at a disadvantage, they'll need to turn & face you. I've found the jab to be much less affective as a southpaw but a good snappy cross punch to bang them with is very handy you something they will very often be vurerable to
Against orthordox people I've had I have alot of success with the following individual techniques:
Lead over hand (somewhere bettween a hook & a jab)
Rear over hand (like a long range hook).
Lead body hook
Inside leg kick to there lead leg (you'll need to step out to your right first).
Rear leg push kick (practice it enough and you can throw it really quick - its powerful & people dont expect it.
Rear leg body kick. (works best if thrown at a deeper angle, more directly into the front of the body)