PDOException: SQLSTATE[42S02]: Base table or view not found

Hi,
I hope you can help. It is very urgent.

I have a Commerce Kickstart installation.
I added Commerce Billy to see how it works.

However, after uninstalling, it still appears in my modules list.
I removed it manually from my server.

I got errors, so I removed all instances in my DB.

But now, when I click on a product, or try to add it to cart, I get the maintenance page.
When I look in my log messages, I see the following error message:

PDOException: SQLSTATE[42S02]: Base table or view not found

saying that the following table is missing:

field_data_field_commerce_billy_cancel_date' doesn't exist: SELECT t.* FROM {field_data_field_commerce_billy_cancel_date} t WHERE (entity_type = :db_condition_placeholder_0) AND (entity_id IN (:db_condition_placeholder_1)) AND (language IN (:db_condition_placeholder_2)) AND (deleted = :db_condition_placeholder_3) ORDER BY delta ASC; Array ( [:db_condition_placeholder_0] => commerce_order [:db_condition_placeholder_1] => 46 [:db_condition_placeholder_2] => und [:db_condition_placeholder_3] => 0 ) in field_sql_storage_field_storage_load() (line 412

I have tried everything.

I did a fresh install of the module, both the dev version and the recommended version.
Nothing is working.

Please help! I have to make the site go live in 3 days :(