It seems unlikely a drywell would have been placed so close to your home. But something is undermining your paving stones. Commercially built drywells are either concrete or high density plastic with a life expectancy of 30 years, but homemade drywells can be made of metal or plastic barrels surrounded by and sometimes filled with coarse stones to allow collected water to seep into surrounding soil. These may have a shorter lifespan.

Do you have any plumbing lines that run under this paving? Even a small leak could cause the shifting of base materials. Do you have a high water table? Gravel and paving tends to sink into consistently wet ground. I would try to find out where outdoor supply and drainage lines run.

Fixing the problem usually requires removing the paving stones that are settling, filling in more sand or gravel to support the stones, then replacing them. Start at the loosest stone, and use a spade to tip up one edge. Ideally you would have a level to raise up any subsidence, a tamper to pack down additional sand or gravel, and a rubber mallet to tap the pavers back into place. But you could use any straight stiff item like a pipe to eyeball low spots. You can use a wide flat board, even an old cutting board, laid over the fill and walked on. Use a short piece of wood placed between the paver and a regular hammer to protect the paver from chipping. It can be very difficult to find someone to make minor repairs; they generally want to completely replace the pavers. Here is an article with video on doing it yourself.