Well, for as long as the Earth exists, your atoms will probably mostly continue to get cycled through various living things and the atmosphere, getting scattered across the globe in the process.
Eventually, the Sun will die and put an end to that (as well as to the Earth). When that happens, your atoms will probably end up mostly scattered about in the resulting planetary nebula, with some doubtless accreting onto the central white dwarf.
The ones on the white dwarf will pretty much just stay there indefinitely, while the ones in the planetary nebula might eventually coalesce into larger nebulae, whence some of them might collapse into new stars or planets. If this happens, then some of the hydrogen atoms will end up getting fused with other hydrogens into helium, but the rest of them will probably be unscathed (though they might end up getting some of their nucleons swapped out in the course of the CNO cycle). And there’s a chance that they’ll end up in a star large enough to fuse them, too.
After those next-generation stars die, some of them will be scattered into space again, and some will accrete onto the stellar remnants (white dwarfs, neutron stars, or black holes). Repeat this process until they’re all accreted onto remnants of some sort or other. The ones on white dwarfs won’t do much, the ones on neutron stars will likely fuse, and the ones that fall into black holes are in all meaningful senses lost.
With time, the white dwarfs and neutron stars will cool to arbitrarily low temperatures. Current models suggest that eventually (after an extremely long time, far longer than the Universe has existed thus far), even protons will decay, and presumably so will everything made up of protons and neutrons. Ultimately, this decay would lead to a mixture of photons and neutrinos, some of which could be traced back to particles which were once in your body.
After an even far longer amount of time, the black holes will evaporate, too, resulting in mostly neutrinos, photons, and gravitons. Unlike with the proton decay, no particular Hawking radiation particle can be traced to any particular particle which fell into the hole, so you’ll just have to settle for claiming fractional ownership (a very small fraction) of each of the resulting particles.
The photons, neutrinos, and gravitons, meanwhile, will just continue through space forever. As the expansion of the Universe continues, the photons and gravitons will be redshifted to arbitrarily low energies, while the neutrinos gradually come to a stop.