Is he loyal or not?

So I know this is bad but I made a fake Ig account and Facebook. And messaged my boyfriend to see if he's cheating or would respond. He is in the military and in a different state so we are long distance and sometimes I just feel like he acts weird and have this gut feeling of something. We've been together for a year. Always been long distance. Point is, I made these account to see if he would tell me about it cus we are best friends or respond. He did not respond to the 2 profiles and read them. But he also told me about it, he said some random girls messaged him. Do you think he's cheating on me just because we are long distance and I would never know? And everytime I ask him hey we should do an open relationship that way you won't cheat on me. And he said **** No is he loyal or not?