Displaying archives by date with month names, not links to months

What I want to do is display links to my old posts on the side of my main page like this:

ARCHIVES
:: Febuary ::
Most recent Feb blog post
Next most recent Feb blog post
Third most recent Feb blog post

:: January ::
Most recent Jan blog post
Next most recent Jan blog post
Third most recent Jan blog post

…and so forth, wherein clicking on the title of a post will take you to that post page. I’ve tried WordPress’s standard monthly archive view plus a number of plugins, but all of them display like this:

ARCHIVES
February
January

Wherein clicking on the month name displays all the posts for that month in their entirety.

I’m sure there’s got to be a way to do this without completely reinventing the wheel, but I am a web designer, not a php coder (though I can find my way around code to a certain degree where necessary), so I need good instructions on how to accomplish this. (So far I haven’t been using any widgets or really going through WordPress’s control panel, I’ve just been installing plugins if necessary and then dropping the code into my own pages where I want it to go.)

Other things I have tried include using this code (which I got from this page):

<ul>
<?php
global $post;
$args = array( 'numberposts' => 5, 'offset'=> 0, 'category' => january );
$myposts = get_posts( $args );
foreach( $myposts as $post ) :	setup_postdata($post); ?>
	<li><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
<?php endforeach; ?>
</ul>
     </ul>

and making each month a category and then adding it by hand. I know it’s a bad workaround, but it allowed me to add in the month name by hand so I had control over it. The problem was that I could only put this code in once and when I tried to put it in again for the next month, it just made both areas display links to both months.