To give you some reassurance too, psychology at university is quite different. Yes, there are still essays, but there are also a number of other forms of assessment, like lab reports, presentations, stats exams and multiple choice exams. You may find that the more individualised support will also improve your essay writing, it certainly did for me!
In some areas of psychology there is only one answer (that we know of), like statistics, neuro-biology, anatomy etc...