Break up, you clearly don’t trust him and now he doesn’t trust you.

Next time, what might help is google how to tell if someone is trustworthy. Read some articles and build a lists of what would most feel like someone was trustworthy to you. Then use that list to either pin point issues that undermine trust and address those problems in the relationship that you have proof of with out invading someone’s privacy, or use it to reassure yourself you can trust them so you don’t go snooping. It won’t solve every problem but it can help you fine tune your efforts such that those lists can either help reassure you that things are ok or they can help pin point problems so you know to address them, rather than just feeling uneasy but not knowing how to approach it.