You could always take a gap year to gain experience to write about in your personal statement for mental health nursing.
But re: psychology. Yes, it's very competitive, but there are things you can do to mitigate it. Having a shining academic record at university is one. Picking up every work opportunity humanly possible during university is also great. If you ingratiate yourself with lecturers at university they'll be very happy to help you and I know a person or two who have managed to participate in some research carried out by their universities by being on friendly terms with lecturers and just asking. All of this helps you stand out in applications. It's also about having a strong mindset and daring the odds and knowing that yes, it's competitive, you might fail a couple of times but if you keep at it you'll probably find a way to succeed. I'm big on chasing dreams so that's what I'd do.