Much can be used with an adjective or with a noun. To be used with an adjective, the adjective has to be comparative, such as happier or shorter. To be used with a noun, it must be a mass noun (uncountable), such as happiness. So, we can say:
I am much happier.
I have much happiness.
(It doesn't work with all mass nouns in all situations; native speakers don't say "with much speed", because we tend to think of speed as having size rather than quantity - so it's "with great speed". But we might still say "without much speed", and "without great speed" would sound a little stilted. Even with happiness I would tend to use great, and I think other native speakers would tend to as well, but much doesn't seem as unnatural with happiness as it does with speed. Trying to break this down to get a clear idea of when to use it with what would be rather a mammoth task.)
"I am much happy" doesn't mean anything except someone who doesn't know English very well is trying to say either "much happier" or "very happy". It has no special or unique meaning, it's just something that would be pretty much universally seen as wrong.