An SM58 shouldn't have much of a noise floor, since it doesn't have an amplifying circuit like a condenser mic does. If you are getting any significant noise, I suspect it is ambient noise from your room.
Per Shure:
As noted, the SM58 is a dynamic microphone and the noise specs are lower than can be typically measured. Dynamic microphones do not have the electrical components that their counterpart condenser microphones have. It is these electrical components that cause a condenser microphone to have a noise floor and signal to noise ratio. Since dynamic microphones do not have these electrical components, they essentially have a noise floor below 5 dB SPL depending on the actual impedance. If the SM58 noise floor is calculated at room temperature, the voltage output is 0.00000032 volts. This noise floor also applies to other Shure dynamic models, like the SM7B, SM57, Beta 56A, Beta 57A, Beta 58A, MV7X and others.
Adding something like a Cloudlifter or FetHead is adding a low noise amplifier, but if your problem is ambient noise, it won't help things. As the saying goes, "it raises all boats equally". In that case the solution is, as stated, getting more of your voice into the microphone.
I think the boxy sound you are hearing is the lack of proximity effect from using the microphone at a distance. The SM58, being a live mic, is designed to be used withing an inch or so of your mouth, and at that distance there's a significant boost in the bass response.