You could create 3 global variables, one for each user selection (e.g. “topic1”, “topic2”, “topic3”). This means you can access their choice throughout the prototype.
In terms of revealing the Next button once they reach enough choices, again you can use those global variables to check if all 3 have been filled (e.g. if none of the 3 equal “null” or whatever empty value you assign to them). So every time users select one topic, not only do you record that choice, but within the same click action you also check how many have been selected so far. If it’s the third choice, then show the button to continue.
You could also track the number of selected topics using a separate variable if it’s easier. Simply add/remove 1 on the total count when users change their selections. After each update to the total count, trigger the relevant action (e.g. if it’s less than 3 show a warning, else show a Next button).
Hope this helps in some way!