It means 'I'm in a lot of trouble.' The basic idea is that there is so much trouble that you could fill a boat with it (metaphorically speaking.) 'I have a lot of trouble...' means something different.

In the U.S. for some reason, "a boatload" has become a slangy colloquial term for "a huge amount." In fact, checking, I see oxforddictionaries.com includes it as "informal: A large amount" under both U.S. and U.K. English. "Wow, we got a boatload of junk mail today." "There are a boatload of things I need to get before we go on our trip." (It is also fairly common for people to use a vulgar variation, "shitload." Don't try to use it yourself. Like most bad language, a non-native speaker won't be able to judge accurately when it is acceptable).