Possible solution:
Double check the paths and php configuration - you might have the imagick.so file in another directory, not the one php is looking for extensions in ?
1) Locate the proper php.ini file - in your phpinfo() page it is pointed which php.ini is actually in use.
2) Make sure you have imagick.so in proper extension dir (the one php really uses). To check the actual path use:
php-config --extension-dir
3) if (1) and (2) are OK, enable the extension in php.ini
extension=imagick.so
4) restart web server, the imagick should be present (loaded) in phpinfo()
Remark #1
Bear in mind that the following also apply
Your extension should compatible with your PHP server in three main attributes:
1- The Zend API number which your PHP server is configured with ( in phpinfo() you can find this number), this number should be the same with your extension header file at build time.
2- The compiler version on your PHP server and your extension must be the same.
3- Thread safety in your PHP server is important. If you use thread-safe server then your extension must be built with php thread-safe library and if you use non-thread safe server you should build your extension with PHP-nts library.
Remark #2
Keep in mind that if an .so file is corrupt, is improper in other ways (incorrect file structure) or depends on files that are missing or not available for load - the extension will not be loaded and made available.
Remark #3
Note that the "php -m" shows modules compiled into php, not the loaded extensions. Try the below for more detailed information:
php -i
EDIT
The provided php error
Module compiled with module API=20090626
PHP compiled with module API=20121212
clearly indicates that you have the module compiled with improper API version that does not match the php. You will need to build the PHP extension manually. The extension you've ended up with seems to be built against a different version of PHP, not your current PHP 5.5.
There are numerous tutorials concerning this topic, just remember to use the proper version of imagick and phpize. This should help you out: http://wiki.dreamhost.com/ImageMagick_and_imagick_php_module_on_shared_hosting