Hi nancymariec,
Yes … most of the chemicals used to make memory foam or gel memory foam (or polyfoam) are petroleum based yes although in some cases a small percentage of the polyols used are derived from plant oils (see post #2 here).
It’s very unlikely that you would be allergic or sensitive to silk.
Talatech is a trade name for Talalay latex made by Latex International. I would keep in mind that all latex (including the latex you are sleeping on) is a “foam” material. There is more about the different types and blends of latex in post #6 here. If you don’t have a latex allergy then latex (of any type or blend) is the least likely of all the foam materials to cause any sensitivity issues.
Phoenix