Here is some info.

Premarin—conjugated equine estrogens—comes from pregnant horses (PREgnant MARes). You probably won't be prescribed that.

Oestrogens can also be synthesised from diosgenins found in yams.

If you're taking injections: Castor oil comes from beans, Benzyl alchohol can come from beaver ass but is synthesised industrially by reacting toluene with oxygen and chlorine, Benzyl benzoate is produced by reacting sodium benzoate with benzyl chloride and sodium benzoate sometimes comes from milk or seafood.

Oestrogen pills contain various inactive ingredients, such as:

silicon dioxide, corn starch, calcium phosphate dihydrate dibasic, lactose monohydrate, magnesium stearate, sodium starch glycolate type A potato, FD&C Blue No. 1, FD&C Yellow No. 5, aluminum oxide

Silicon dioxide is sand.

Corn starch comes from corn.

Calcium phosphate is found in bones but I have no idea how it gets synthesized from phytic acid and calcium chloride on an industrial scale.

Dihydrate dibasic is produced from calcium hydroxide and phosphoric acid; calcium hydroxide is made from calcium oxide which is made from either lime or sometimes seashells. Phosphoric acid comes from either rocks or coal.

Lactose monohydrate as you may have feared is milk.

Magnesium stearate is made out of magnesium (a metal) and sodium stearate. Sodium stearate can be produced from animal tallow.

Sodium starch glycolate type A potato—much like gnocchis—ist potatoes.

FD&C Blue No. 1 is synthetic.
FD&C Yellow No. 5 is also synthetic. I have no idea how they make it.

Aluminum oxide is rubies; they extract it from aluminium ore