I'm not sure Hostmonster will redirect your name servers. Since your domain name is managed by another party they cannot access them.
You could redirect the name servers yourself but you do not have any files in your hostmonster public_html directory to redirect them to....
Steps I would suggest.
Go to cpanel
go to domains
go to transfer domains
they have a video
https://www.hostmonster.com/cgi/help/transfer
hostmonster will transfer your domain to them. Then you have full control of everything at hostmonster.
Now do you want another website or do you want to use your domain for a wordpress site?
If website, build you website on your computer and upload it to the public_html directory. If a wordpress site, go to software services, wordpress, install at the bottom of the page.
If you use wordpress you will have to upload all your images to your wordpress blog. Be careful you will get a totally clean blog and you will start from scratch....
I would recommend transferring your domain from the other guys and downloading and uploading your existing site into hostmonster as a start.
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