We investigate the transition from sub-Poissonian to super-Poissonian values of the zero-temperature shot noise power of a resonant double barrier of macroscopic cross-section. This transition occurs for driving voltages which are sufficiently strong to bring the system near an instability threshold. It is shown that interactions in combination with the energy dependence of the tunneling rates dramatically affect the noise level in such a system. Interaction-induced fluctuations of the band bottom of the well contribute to the noise and lead to a new energy in the Fano factor. They can enhance the noise to super-Poissonian values in a voltage range preceding the instability threshold of the system. At low voltages, interactions may either enhance or suppress the noise compared to the the non-interacting case.