The third boss in MrT is unique because there is little to no aggro table. It is supposed to be more of a 5v5 pvp style fight. The adds will usually go for the healer regardless of how much threat anyone else has on them, which is why cc is so important in that instance.
Keeping Prayer of Mending up can help with the raid taking damage. I don't really know of any specific things that you can do to make you instantly better-it just takes practice. As a priest, one of your main strengths as a healer is that you've got a lot of different options for healing spells. Knowing the right one to use on the right target is something that you will learn running, and wiping in, heroics.
A big thing when you're the only healer is knowing what is going on around you, who is taking damage, and who should take priority. Usually I go Tank>Healer>DPS. There are addons that can show you who is being targeted by enemy units. That can usually give you a second or so warning as to who will be taking some damage, and let you get a heal started ahead of time.
Its tough to know exactly whats happening without being there. I'd be more than happy to respec to balance and run some heroics with you. This way I'll be able to see what is going on, offer any suggestions, and backup heal if things get sticky during boss fights.
Here's a link to the build that I like using for 5-mans:
http://www.wowhead.com/?talent=bxgh0hZfxtcfMqV0VoYou're fine the way you are though. I just like having a bit bigger heals, as well as Circle of Healing, in exchange for the increased spirit.