I searched everywhere but I can't find a healer build. For those who don't know, a healer was a playable class in morrowind and oblivion http://elderscrolls.wikia.com/wiki/Healer

Race: Imperial or Breton

I will be using:
-Restoration
-Alchemy
-Speech
-Alteration
-illusion
-Destruction

My question is it viable to just use destruction and illusion to defeat enemies, I find destruction weak, I was thinking of one handed but I don't wear armour so it may be a real challenge.

Now because I will be a healer and a good character I will only be joining the college of Winterhold. No daedric quests and only doing good quests

Anyone got advice or have played with these skills at high levels (Is it viable etc)?

Destruction will serve you fine at low difficulties and only then at lowish levels.

Don't forget that Alteration has armour spells, and they're decent with the right perks.
My one-handed/block/restoration character uses them, and she does fine.

Take out destruction/speech and use maces and enchanting.

I would question the use of Destruction if you're really trying to make a 'healer' character. With that and all the other schools minus Conjuration, it sounds to me like, well, just a standard Mage! You might get an informative kick out of PC Gamers entertaining 'An Illusionist in Skyrim' : http://www.pcgamer.com/tag/an-illusionist-in-skyrim/ : it isn't what you're planning to do, of course, but it does at least show that it is possible to progress to some extent without using direct-damage skills. If you ask me, I'd use Restoration, Illusion, Conjuration, Speech and precious little else. It could be fun!

Yeah i would take out destruction as well and use illusion, also make sure you take advantage of a good follower