I have been wearing panties just about everyday for almost 2 months (my wife got me started), and I wear a bra every so often too. She will tell me if it looks obvious or not, and I either take it off or change my shirt (we have 2 teens and the oldest is VERY observant). I am in my beginning stages or everything, and luckily my career allows me to limit interactions with others. I now have a decent (small) wardrobe of women's clothing, and as for now only wear them when it's just me and the wife (except one pair of pj pants that pass as neutral). I too have felt my dysphoria go away while I am wearing women's clothes, but it does return when I have to re-assume "guy mode".
But I want to ask a side question too. I have always felt dysphoria towards my testes, but not my main organ (still learning the do's and don'ts of the rules). I have noticed that everyday that I wear panties, I feel myself becoming more dysphoric towards the whole package (more so the testes, they get in the way). Has anyone else had this, or notice this happening (or happen) to them?