[PinkMilk]

I would suggest a database query to search:

SELECT * FROM prefix_post WHERE pagetext LIKE '%www.photobucket.com%';

% are wild cards meaning you are likely to get more than one result, if you know the exact string of text your looking for they can be removed, they simply help with not having to worry about knowing weather the url starts with http or https in the first instance and any thing after in the second.

or to search and replace:

UPDATE prefix_post SET pagetext = REPLACE(pagetext, 'photobucket', 'tinypic');

if you have table prefixes you will need to add these to query lines as highlighted else remove.

Always remember to make backup of db.