Hope it won't die

It froze? How cold were the temperatures?

I don't know exactly, my friend bought me this flower, but on outdoor market. I think it was about 28°F.

For this particular plant, one would expect the part of the plant above the distal node (farthest from the roots) to die back to that node, and the dead part would make an angular line. Let me use the image below as a visual aid:

What you have is essentially the same as the image labeled 'cut made too high'. The stub left above the top bud would be expected to die back to just below the angular cut on the image labeled 'correct'. The reason the cut is made slightly higher than necessary (on 'correct') is to make sure that after the pruning cut is made, the tissue below the pruning cut cannot dry out such that it kills the bud.

Now, I understand we're not talking about pruning. I used the example so you might see what I'm seeing - that the necrotic (dead) tissue seen in your images is not only lower than it would be expected, it also looks like the basal (at the base) area of both branches are affected. This could be resultant of the chill injury, but the additional die back and the chlorotic (yellow) streak that continues down the stem are concerning.

The impression I'm left with is, you have something fungal going on and the disease is moving systemically in the plant. It might have started in the root system, which I most suspect, or there is some chance it originated in tissues damaged by chill injury. At this point, there is little you can do but make the patient comfortable (proper light, temps, watering, fertilizing) and wait to see what Mother Nature has in mind. We're all hoping for the best outcome.

Al