Why are the blueberries in my blueberry muffins not melting?
Honey versus sugar has nothing to do with your berries bursting or not. 

Assuming you are in the northern hemisphere you are getting out of season fruit as it is winter. Your blueberries are either greenhouse grown or have travelled halfway around the world from somewhere warm enough to grown them. Out of season blueberries tend to have less flavor and have thicker skins because they are not ripe.  They cannot be ripe when picked because they will rot before they make the trip from wherever they are grown, so they are picked while still underripe. 

I would suggest buying frozen instead. Frozen berries are picked when ripe and then frozen right away, so usually taste better than fresh ones you get in the middle of winter. Freezing also weakens the skins, so they burst more reliably. Frozen are also much cheaper. In fact that's what I would suggest doing to fresh ones to make their skins burst when baked - freeze then thaw them, so you may as well save some cash and get a better tasting result by buying them frozen in the first place.