Do I need to apply for greencard to get EAD?

[luckywilson]

Please help me I'm really confused. I just married an American, I have an H-1b visa and never had a fiance visa. My H-1b will run out in a month or two and I want to get my EAD. My question is can I get it without applying for adjustment of status? Because I want to do it as soon as possible.
But on the form for the EAD I'm not sure what category I fall into - I don't have a fiance visa - am I a non-immigrant spouse of a US citizen?

Any advise would be great.

Thanks.