There is no fiberglass in cigarette filters, it's a persistent urban myth. Snopes has an article on the origins of the myth. The vast majority of cigarette filters (both tailor made cig filters and rollie filters) are made of cellulose acetate from wood pulp. In Australia cigarette manufacturers must post the entire ingredients of their products online, including the composition of the filter, so it's easy enough to check out your fave brand.
The study below from the Harm Reduction Journal compared cigarette filter, cotton ball and micron filter. They didn't find much difference between cotton and cigarette filtering, except that possibly the cotton retained a little bit more of the drug, but nothing significant.
Effect of filtration on morphine and particle content of injections prepared from slow-release oral morphine tablets