Would it be OK to stalk my ex's emails to see what he's up to? Because I did.
Uh, that's creepy. Did you suspect he was up to something?
Yes, and I was right. He was up to something and it made me feel like shit to find out for sure.
If you are in a relationship with someone, it is best not to hide things from them. But if it was your ex you are snooping on, you don't really have the right to know what he's up to anymore; you're no longer together. You shouldn't give in to the urge to snoop in someone else's email; as you found out, it just makes you feel bad when your suspicions are confirmed.
I can't just not look after doing this research.
You need to move on from your ex. It will be much better for your mental health.