I checked a few widgets for adding Twitter feeds to your site, but I think that one of the nicest ways of doing this uses Twitter’s own method.

You can add a Twitter feed like this as follows:

1. Sign in to your twitter account
2. Go to https://twitter.com/settings/widgets/new
   
3. Configure the options you’d like – keep it simple, and probably use the ‘light’ theme.  Keep the height down – maybe try 300 ?
4. Click ‘Create Widget’ (or ‘Save Changes’)  and then copy all of the code from the box at bottom right.
5. Sign in to your WordPress site.
6. In the dashboard select Appearance > Widgets
7. Drag a new Text widget either to the Showcase sidebar (many medicine sits use this on their frontpage) or the main sidebar.
8. Open the new text widget, leave Title blank and paste your code into the main field. Click ‘Save’
9. Test the result on your website.

Go back to step 2 if you want to make further adustments.