Unfortunately, many of the problems you had with stick will follow you with flux core. Flux core as a process was intended to be more productive version of stick welding. It requires more heat than gas shielded mig to burn the flux to generate the shielding gases.
If you can swing the extra cost for a solid wire mig welder and shielding gas, you will have a much easier time with any automotive welding. You might be able to struggle through an exhaust will flux core, but it's going to be a struggle for sure.