Thanks to all who had a look at the tune. And sorry about the lack of information from me.

Anahata - I am very bad at music theory (so treat everything I say in that area with great care) ...
Key should be one # - whatever that key is called.

I only can play tunes in # and ## on my tin whistles - and only know that there is one difference (afaik that's c vs. c#) when fingering it on the tin whistle. Comparing with tunes that have one or two ## it needs the same fingering for that c/c# (I really am quite bad at music theory) as in tunes with just one #.

I've tried a bit with the rhythm (by having the notation software play it to me. It still doesn't fit what's in my mind, but much closer.

new picture of tune

leeneia, I'm not sure about any F# in there (see above), it should have one # at the start of the line ;-)

I found "Away in a Manger" at the Tune finder - the first part seems to be the same, but after that, it is quite different.
It doesn't have Jesu Bambino.

John Giok, the Flower of Scotland is quite different.