It might not be "morphing" precisely; it may be that once you've resolved a problem, your mind automatically turns to the next problem and begins dwelling on it, instead. This problem would have given you this anxiety if your mind hadn't been busy feeling anxious about the other things.
It happens to me, too. Really, I think this is why people have "first world problems": because whatever problem they consider most serious in the moment carries a great deal of weight, even if, in the grand scheme of things, it may not be very important.
When you solve serious problems, though, and you have more happiness in your life, the happiness can outweigh the anxiety you get from these smaller problems, so on the whole, you life can seem good, even if there are still things that worry or annoy you.
Maybe instead of using your tools on the problem directly, try focusing on things that relate to the problem, that aggravate it or that prevent you from managing it more effectively. I had a health problem that bothered me that I couldn't manage properly because my anxiety prevented me from seeing a doctor. Once I did force myself to see a doctor, I was able to better manage the problem. I had to focus on the anxiety preventing me from dealing with the problem, instead of the problem itself. There may be things connected to your problem that your tools can fix that will make the problem itself less pressing.
In science, ideology tends to corrupt; absolute ideology [corrupts] absolutely" - Robert Nisbet