Most often the best way to stick 2 pieces of fabric together is sewing them. In the special case of wool you can also felt them together by placing both pieces of fabric on a soft foam surface or plush towel and then repeatedly stabbing them with a felting needle. That requires no chemicals at all and you can decide how well they stick together by stabbing them more. You can see in this article how a red blossom is felted onto a pink scarf.
If in doubt, use transparent construction silicone. It's reasonably cheap, doesn't produce any toxic chemicals (although it stinks of vinegar while curing), and bonds to almost anything almost forever.
It's ideal to put a few tiny blobs of silicone on one piece of wool and then gently push the other cloth into it, but only so far that the silicone bonds to the outer fibres. You don't want to push the silicone through the fibres. If you want to cover a wider area in silicone, use a disposable scraper or plastic object to spread it out. The surface takes only a few minutes to dry, so you might need to split the area into smaller portions. Dip your fingers in some water mixed with dish soap to stop the silicone from sticking to them.
Some alternatives are:
- Plain PVA glue (aka Elmers glue, wood glue, white glue): unbeatably cheap, non-toxic, dries clear, water soluable even after it dries, but may leave stains in the fabric even after drying.
- Acryllic glue (like ModPodge, clear acryllic medium, construction acryllic glue): cheap, non-toxic, somewhat water resistant, but may also leave stains in the fabric.
A word of caution: moths love eating wool in a mostly undisturbed indoor environment. The eco-friendly solution is either lavendar blossoms or cedar wood, but you'll have to renew the repellant each year. If you're making something like a collage, try to incorporate a little pocket where you can place the repellant directly into the artwork.
