Different feminine products can cause different reactions. Tampons with strings when ingested; strings can become entangled and cause an obstruction just by the size of the created mass. Slightly used products of the same nature can singularly absorb upper and lower GI fluids and expand in such proportions to create a blockage.
Some pads may have "additives" that combat odor or increase absorbability; these may cause a irritable tummy or in some cases severe upper/lower GI reaction.
My vet never heard of a toxic reaction to these products, but she never the less, doesn't discount it when it comes to dogs with allergic reactions from an "unknown substance" (Some owners are less forth coming with the true info when asked "what did your dog eat recently" question. Feminine products, condoms, crotches from underwear, sex toys, stimulant products, etc…aren't documented much because the owner is not forth coming with the vital info.)
That said...syrup of ipecac should be a home owner staple. Peroxide is another. Not to disrespect anyone who has posted before me, but educate yourselves as to when, and when not to induce vomiting. Inducing vomiting in some instances, can sometimes cause more damage, and perhaps be fatal.
Following a copy and paste from a vet….....
It is possible to induce vomiting using hydrogen peroxide given in small amounts until the dog vomits or by using syrup of ipecac (it takes about 1 teaspoon of ipecac syrup per 10 lbs. of body weigh to induce vomiting, on the average so it can be hard to give enough of this --- and overdosage can cause heart problems so it does have to be measured). Apomorphine is a good choice for inducing vomiting, too -- but usually only available through your vet and it is pretty expensive.