Your first step in this situation should be to create a segment of customers who received the first campaign. This segment will then be excluded from your secondary send to ensure that you don’t double email any profiles.
To create this segment, head to your Lists & Segments tab and click to create a new segment. Once you have named your segment, choose the following definition: What someone has done (not done) > Received Email > at least once, then filter by your Campaign Name
When you create your second campaign, choose to target the same lists or segments from the original send and exclude the segment that you just created to ensure that customers do not receive multiple emails.