In general characterization, I wouldn't even say wouldn't/couldn't talk about - at the start of the Avengers, to me he just looks emotionally drained. Which...he's a secret field agent, and a sniper - he's been killing people for a loooong time, and he's hardly a sociopath (if he was, he just wouldn't have his security clearance). And that kind of business, and those kinds of missions, would just take their toll. Even if he's going to a shrink, the espionage business is consuming. So, there is a decent lot of material to work with without it being a secret, if you wanted.
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:)! glad to help.