Traveling out of my province (COVID-19 Advice)

Hi, I don't know if anybody can help, but i'm trying to find out if its possible to get permission to leave my province (Malaga).

My situation is a little unusual. My main habitual residence is my house in the Malaga area but at the start of March i signed a 3 month rental contract on a room in Madrid which i was going to use while taking a course and potentially looking for work there. As it turned out, Madrid fast started becoming hard hit by COVID-19 and after less than 2 weeks, a couple of days before lockdown was enforced, I decided to come back to Malaga to wait it out.

I am now in the situation where my contract on the Madrid room runs out at the end of the month and I still have a lot of my stuff there which I'll need to collect in order to vacate the room. I've been reading the lockdown rules and understand that you can't travel outside your province unless you have 'justified cause'. But I'm struggling to find information to understand if my reason is valid , if i would need to get some kind of written letter or permit to do it and who I would need to speak to to get this. Can anyone shed any light on this.