JB Weld is an epoxy.
There are different formulas for different applications.
Some 'glues' will work, if you get one for that application.
Thing is, when you buy a special glue or epoxy, the good ones might cost more than the replacement head.
If you are going to try to 'glue' it back in place keep a few things in mind.
The mating areas must be clean and dry.
After cleaning the parts, lightly brush or wipe some rubbing alcohol on them.
If possible, scuff the areas where the adhesive will go.
Too much adhesive could make things worse.
Use a toothpick or other fine instrument to apply the adhesive only to the area where it needs fastened.
Glues & epoxies work best if you press the part into place, then lift it away and press it in place again.
You can also apply a small amount to each bonding surface.
Once you press the parts together, wipe away any excess.
Follow the instructions on the adhesive packaging.
Let it dry a bit longer than the recommended time.
The bonding agent should be fully cured for best results.
If these are really small parts, you might want to consider using a little lotion on your fingers. It might keep the glue from sticking the parts to your fingers as you work.
You can also compound eye glasses so you can see small things better. You might look goofy wearing two pairs of glasses but it does help magnify what you are looking at.
Also consider a small LED flashlight and if possible some type of holding device to hold the big part while you work with the small part.
Shower heads are not really expensive.
It could be kinda tough to find one you will like tho, especially if there are limited hardware stores in your area. You can sometimes find a few in department stores (hardware/plumbing section) and some thrift 'dollar' stores also carry a few (low quality ones).
'Super Glue' has many different formulas for different applications. Again, you are limited by availability. The package will tell you which materials it is designed to bond with.
I have two different shower heads on a diverter valve.
One is low volume / high pressure, the other is an adjustable pulse head with different settings.