I don't want to want to wear armor yet. I've found some clothes I really like. I want to know if just carrying a shield will build up my heavy armor skill? Also will it build up my block skill as well when used in combat?

Yes, when it gets hit your Heavy Armor skill will increase, and when you successfully Block, the Block skill will increase.

That's great! Thanks!

If the shield is made of a heavy armor type, like steel, Daedric or Ebony, etc., then using the shield improves heavy armor skill, too. If it is some other type of material then it improves light armor or medium armor skill.