I changed my guitar strings yesterday and the new ones just don’t hold in tune. After less than a minute they go out of tune and I’ve noticed that my bridge is getting higher and higher as I try to tight the strings. I’m seriously worried about this situation because I’m a beginner guitarist and I’ve been reading that taking all you strings off and leaving the neck without tension for a few days damages the guitar (which was what I did in order to clean the fretboard). I had never restringed a guitar and I just don’t know wether the problem is having left the neck with no tension for days or if I restringed badly. My guitar is a Fender Stratocaster. Please help.
There could be many issues with your guitar that may cause these issues, but off the top of my head, it just sounds like your new strings haven't fully stretched yet. If you put new strings on a guitar or bass, they will stretch a little from where you first tuned them, after playing and retuning, you should find that they hold their tune a lot better. Unless of course, as some commenters have mentioned, there are bridge issues. I would suggest lightly pulling on each string once you have them in tune for the first time to stretch them a little, of course, be gentle you don't want them to break straight away, and then retune, maybe a little more stretching to the point where after pulling on them again they do not go out of tune quite so much. If this is the issue, you should not have as many tuning issues.
I had originally deleted my answer but decided to edit it and post something because there seems to be a lot of focus on string slippage but first, steel strings don’t take long to stretch if they are installed correctly and second, stretching strings won’t cause a bridge to rise.
The fact that the bridge is rising tells me the real issue is your new strings are heavier and/or have more tension and are pulling harder on the bridge and tremolo system. You could try a lighter gauge set but if you want to use the ones you bought then you need to make some adjustments.
I suggested searching “adjust tremolo Stratocaster” in my comment. There’s a good chance you can solve your problem by either putting more tension on the springs with the trem claw, the metal piece the springs are anchored to that is held in place with 2 wood screws, or adding a spring if your guitar only has 2 installed. Watch a few videos and follow the advice of the various skilled luthiers who post useful information for us do-it-yourselfers.