As Notso Fantastic says TOGA only disarms when another mode is selected, normaly FLCH. You could also select VNAV (THR REF, VNANV SPD) if the Go-around is loaded in the active route.
The TOGA roll command remains the active mode until HDG SEL or LNAV is selected. So if you do nothing you will continue straight ahead for ever!!
A small correction to Notso's post, if you do nothing in pitch then when the MCP altitiude (the GA altitude) is reached the pitch mode becomes ALT (hold). Thats fine, however the A/T remains in THR (or THR REF) until SPD is selected. This could catch you out, with the aircraft rapidly accelerating toward the max flap speed! But, 5 kts before the max operating speed is reached speed protection will kick in to prevent you bending metal, very clever.
This is why, as Notso said, we select FLCH, then SPD, then dial in 200 kts or whatever you want.
It sounds like you have a sim ride coming up, best of luck.