These days main purpose of a healer in ESO has majorly moved from healing and into buffing. More experienced people will rarely, if ever, need a healer in base game dungeons, even vet, at least if there's a taunting tank around. Even in vet dlc's you can do a lot of them without a healer (a lot of vet dlc's suffer from a different issue - in an attempt to make them harder ZOS made like 90% of the damage (Thurvokun in Fang Lair and Zaan in Scalecaller Peak would be good examples of that) one shot you so you either avoid it entirely, in which case you need no healer, or you don't avoid it and inevitably die, in which case healer can't help you anyway), but what a good healer can bring to the group is invalueable. The amazing sustain, the juicy damage buffs...as a dps, I majorly prefer running with a healer than running 3 dps - not for the heals, I can keep myself up, but for the invalueable buffs.

Not saying that to make you feel bad, it sounds like you're just in the start of your journey and doing just fine there, just thought I'd give some pointers for lateron:)