About her burnout compared to morganas pool:
A friend just told me i should clarify, yes the two do the same amount of base damage, but using the average build, morgana will have more damage early game with ap amount as compared to extra damage for shyvana.

I would also personally get some different quints, she does have a ranged spell and can farm decently with it and can still use her q if she is solo top, the quints you have are really only useful for a little extra lane sustain, otherwise they dont really help.

Study up on her a little more, seems your not quite knowledgeable about all her skills and abilities yet. Ex) her ultimate gives her double the passive bonuses to armor and magic d, so using her ult in a 1v1 can be very useful. Obviously you should try to save it for using it as an escape mechanism if you get ganked after the 1v1, but you shouldnt rule out using it for 1v1s, it can be VERY helpful to get all that extra armor and magic d and can easily turn a fight. Also, her burnout is not a good farming tool until mid/late game, seeing as it does not do that much damage by itself early game (a little less than morgs death pool).