Don't worry too much about it. Yoshi-P himself has stated they generally don't balance content around having a necessity for healers to DPS. It's us, the players, who may want you to DPS. That being said, if you're not comfortable about it, then don't. For you, as a SCH, you'll have the easiest time learning to DPS. The fairy heals for a huge portion of your overall healing. As you level, that thing IS your party healer lol. Try running something like Sastasha or Totorak and you'll notice you almost never need to heal as SCH, since your fairy will pretty much overheal. Those low lvl dungeons are also an easy training tool to learning how to manually control your fairy to heal on command (alongside its auto-heal script), since as you're DPSing, you can control it as a separate character with its own GCD.
Bottomline though, don't worry about DPSing if you don't want to. It helps, but it's far from mandatory in most groups, outside of things like Savage mode raids. And the only reason that is needed is because we want to clear it sooner than the devs intend for us to. Sometimes, like occasions like that or a bad dungeon group, the DPS will be lacking and can't keep up with a DPS check mechanic. Healers throwing out some damage can help save the party, but again... not really your responsibility.
It's the role itself that you need to consider. In most traditional RPGs, the healer is NOT a damage source. They may have a mediocre spell or two that is intended for damage, but you just basically keep them in the back and heal when needed since their damage output is pathetic. That's why they're there, to heal, after all. It's only the modernized MMORPGs that popularized the idea of healers doing damage as part of a community expectation. The devs, however, will rarely ever create content with the expectation that healers must DPS for everything.