Is there a way to see the people that converted through my campaign?
Yes, of course. On your conversions screen (Marketing>Conversions) you can click on the 'More' button.
You will then be able to see all the visitors that converted, their name, how many entries they have, the country they are from, their contact details (if they left any) and when this conversion was completed.
You can also view the profile for each of those users, or mark them as Favourites. Finally, you can export this list to any of the formats available (CSV, PDF, Excel), copy the list or print it.