I've had a high fantasy/fictional universe building up in my head for years, however it's timeline extends much further beyond the classic middle ages, going up to modern times and having it's own ancient times as well. I'm currently working on Elven technology in the modern period of this universe, and their primary strengths are in biotechnology, agriculture, artwork and literature, precision-based tasks, herbal medicine, bioplastics, and martial arts. They would have their standard allergy to Iron like in other fantasy universes, although this would be more restricted to pure iron, they would still have iron-based blood. However, other than essential nutrient minerals and naturally occurring mithral-aluminum ores, Heavy metals such as iron, lead, copper etc are exceedingly scarce in their home environment, and this quickly became apparent as firearms and other gunpowder weapons became more and more advanced.
So I'm thinking about giving them special, high-gravity bio-polymer bullets, preferably from a renewable source, that can achieve densities rivaling that of heavy metals WITHOUT just filling normal plastic with metal fillers. The other components of the cartridge should be feasible enough(caseless rounds and polymer-cased rounds exist in real life, and there are propellants derived from organic compounds like nitrocellulose) to not stress me out about authenticity. It's just the projectile or bullet itself I'm having issues theorizing without using some form of high density metal/mineral, and so far I haven't found any real life polymers with high enough density to reference to. I know this is probably putting way too much detail into it, but that's the whole point, I want it to be detailed and actually look like what life would be like in a fantasy universe. Magic is out of the question either, because while it could counter this issue in some way, it's difficult and dangerous to learn, while mass production using magic is virtually impossible due to the amount of mages of high enough experience required. I just want to confirm if a polymer of these characteristics is scientifically plausible.
Edit: My apologies for the wall of text, This is my first post. I tried to squeeze it into paragraphs to the best of my ability. To be more specific, I mainly just want to come up with an effective ammunition type that is meant to be sustainably produced, disposable, but effective enough for the military, metal ammunition would still probably be used in other situations. Also, on the topic of carbon as everyone so far has been mentioning diamonds, There are "superdense carbon allotropes" that apparently can go as high as 7.06 g/cm3(according to https://en.wikipedia.org/wiki/Superdense_carbon_allotropes), but these are produced under very high pressures which is probably gonna be too expensive and energy consumptive, plus I assume that they are going to be at least as hard as diamond or even harder, so the bullets would need to be coated with a soft substance(like real life plastic coated bullets) or else it would damage the barrel. And it's still not as dense as lead or copper, so the bullet would have to be longer as well in order to achieve similar weight.