People have different ways of thinking about music, so don't beat yourself up too much. I suspect there are many wonderful musicians who can't play by ear or improvise.
However, here's how I would start with the jingle bells problem. I'm assuming a piano here.
Try to play Jingle Bells monophonically, in C major using only the white keys. Do it by trial and error. If you find you need a black key, then you've started on the wrong note. Start on a different note. Think about when you're playing a C. That's the tonic. Think about how the tonic sounds; the third; the fifth -- important intervals
You can accompany yourself with the chords C, F and G. "The three chord trick". At first just play them as block chords, e.g. for the C chord, plonk down on C, E, G. Trial and error again. Hopefully you can hear when there should be a chord change. Try one of the three chords, until it sounds right. If you get bored of block chords, arpeggiate, or whatever. You can go by what sounds right, but once you've found it, reason about the chord you've chosen. Which notes in the melody match the notes in the chord? Which notes do not? Are those notes on the beat? Long or short? Are they a deliberate discord? etc.
Now try transposing it to different keys. If you've not practised any scales yet, now would be a good time to start. Learn scales in the order they're introduced in a beginner's piano book, and try to play Jingle Bells by ear in those scales in the same order.
By now, you're probably not really playing Jingle Bells by ear any more -- you're playing it by memory. Try playing folk/blues/rock/pop standards. "Go Tell Aunt Dinah". "Louie Louie" and so on. Anything that fits those three chords. One snag: you might not yet know how to tell something's going to fit the three chords. If there's someone to ask, go ahead. Otherwise, just try, and if there's a spot in the song where none of the three chords fit, ditch that song for now. Concentrate on the low hanging fruit, until you can play a three-chord song by ear, with block chords, reasonably easily.
Add in chords. Those songs ditched because they had a fourth chord -- bring them back into the mix, and try and find the right one. Stick with the simple folk/blues/rock/pop standards, you're hoping to find ones with just one new chord. In the key of C, you're most likely to next encounter an Am but it could be anything. At this simple level, there are really only 24 chords to try (all the majors, all the minors), and you can narrow that down to the seven that can be played on the white keys. It's OK to cheat and look in a book/web page, but try to learn from that for next time.
And really, it's up to you where you go from there, and it depends on the way your mind works.
You might find that you're most comfortable stringing chords together, and noodling on top using the intervals you've put into muscle memory -- not quite knowing how it will sound, but knowing it will sound OK.
You might find that you can hear something in your head, and be able to play it the way you hear it.
You might not be the type of person who naturally falls into either of these, but you'll be able to contextualise the sheet music you play ("I see, Chopin has me playing a Bb over a Gm chord because that's the third in Gm")