You've relied too much on doing what the sheet tells you! You need to start using your ears a lot more! Let's take a three chord wonder, of which there must be tens of thousands, not all the same, obviously.
You need to play along to the first chord - we'll call that I, generally the first one in a song, to establish a 'home' feel. Whilst playing, listen to where the melody is going. At some point, often at the beginning of a new line, new sentence/phrase sung,or bar, it will feel like the chord you're on now isn't going to fit the next part. Now, in a three chord song, that gives you a 50:50. It'll either be IV or V. That's where the experience of playing, and being able to listen, not just hear, comes in. O.k., you make the choice and it's the wrong one! Now you know what the right one is!
Stay on that till you feel the next change coming up. Still 50:50! If you eventually found the right first change was to IV, then the next change has to be either V, or back to I. If it feels like a small step, chances are it's to V, or maybe it feels like a bigger step - back to I. If so, it should feel like you're back home, albeit for a short time.
Start with things you haven't played before from sheets, maybe Happy B'day, Silent Night, etc. Choose a key, sing along, or get buddy to, slowly, and stop just as you get to where you feel the change coming. 50:50 isn't a bad bet, but eventually you'll start thinking 'no, it won't be the previous chord again, so it's moving on'. Or not.
When you get better at that, start adding the ii, iii and vi (the minors - we write them using small R.N.). Again, the choices aren't huge. If you're on a major, and it feels like the next won't be - it's 33%. Still good odds!
At the same time as all this, try to familiarise yourself with how each change feels. Maybe I>IV feels like it's going up, while I>V goes down. You'll have to decide on that yourself. It's a bit like trying to describe what an orange tastes like!
EDIT - When you get onto barre chords on guitar, whoich will be necessary in several keys, the I, IV and V are more obvious. Using E and A shapes, the I is an E shape on x fret, IV an A shape on the same x fret, while V is an A shape on x+2 fret. No need even to be thinking what the chords are called - that's academic in this situation. That's just one simple way to think of what comes next, within a two fret range.