Sounds like a pretty normal first LD to me, i know my first was exactly like that hehe.

To answer your question, yes an LD is when you feel like your walking around awake, yet you know your dreaming and can mold the dream into what you want.

My advice is just keep trying and you'll get there, If your not keeping a dream journal, start one up, they improve your recall so much and will seriously help you realise when your dreaming.

(By the way, it will feel slightly different from reality.. Because you'll know it isn't real)