My tzitzit got caught on the door handle as I left a room.
I heard some sort of snap but couldn’t see what was wrong, until after examining the tzitzit I noticed that on one of the corners only two threads went through the hole rather than the four on the other corners.
Assuming that these were whatever strings I had heard snapping, I pulled these strings through the eyelet and onto two other strings (though not necessarily the ones they had broken away from).
Has this ‘fixed’ the tzitzit or should I buy a new one?
From your question, I didn’t understand clearly how you fixed the tzitzit.
If two of the strings tore off the tztizit, there is nothing to do other than insert another two new strings through the eyelet, and to tie them with the others. Folding the existing two does not help.
Please clarify if you need more details.