Yeah, if your group is in combat and you cast a healing spell, it increases the level of threat you have against all enemies your group is fighting. This can be especially dangerous if the tank has not used some form of AoE effect to at least get some level of threat against all mobs you're fighting (Thunder Clap for warrior tanks, consecration for pally tanks, etc), as one heal can frequently pull one or more mobs to you, the poor defenseless healer. One of the keys to healing safely and efficiently is to hold off on that first heal until all mobs that have been aggroed have been tagged so you can fire off your spells without immediately pulling a bunch of mobs to you, which makes more work for you and your party in trying to get them off you while you heal yourself and them.
Granted, it's not always possible to wait very long to pop that first heal (this is especially true if your tank is somewhat undergeared for the instance being run), so that's what you should save spells like PW:S (priests) and divine protection (pallys) for. In the former case, it'll at least give the tank a few extra seconds to pick up the mobs (which can save your group), and in the latter, it can send the mobs from you directly to the next highest person on their threat list.
So yeah, just keep plugging away at it, if you find people that are decent and you enjoy running with, invite them along again. Who knows, you might even find a full 5-man group that'll get together and run a bunch of instances together, which will make things easier for everyone every time.