@JaneyJimplin
My OH suddenly found me and the kids really hard work, and would take himself off in a sulk on his days off. Maybe because being stuck at home with me was depressing as fuck compared to taking his fancy woman out for expensive dinners, or maybe because stewing on my flaws helped him justify his deceit? Like, "the wife's a nag and the kids are terrors, no wonder I'm seeking solace in another vagina, I'm only human etc."
LOL at this.
So accurate for SOME men! 
OP, of course YANBU to be worried. Who the fuck deletes all their messages as soon as they come into their inbox? Only someone trying to hide something (more often than not!) I have texts on my mobile phone from as far back as a year ago!
Although I do know a woman (at work) whose DH seemed to enjoy flirting with other women, and being a shoulder to cry on for female colleagues, and it made her really insecure and quite upset. He had a big puffed up chest already, with the women at work thinking he was so nice. 
But it was a double bonus that his wife (my colleague) was insecure and a bit upset by it (as he loved it when she was jealous as it showed she cared.. fucking weirdo!
) He was never interested in these women romantically, but loved the attention, and his wife being insecure about it.
So he used to delete any mobile phone messages he sent or received (AND he did the same with his emails.) He also had a PIN on his briefcase, and a password on his laptop. Not because anything was going on, but because he wanted his wife to THINK there was..... to keep her on her toes.
It backfired a bit when my colleague got sick of his over-friendliness, and decided to start flirting with men, and showing an interest in them, and she ended up falling for someone else, and left the twat of a DH.
I doubt the OP's DH is doing this though - I mean, pretending he is up to something to make her insecure and grateful he is with her. Sounds like he is definitely up to no good. Especially as he is being moody and distant, and trying to make you feel like YOU are the problem! 
I would keep a VERRRRRY close eye on him @Laurry and wait til you have concrete proof. I feel for you, I am sorry........ I hope you're OK, and nothing is going on! 