Well, your clitty going hard isn't really what I'd call a problem. It's normal for CD's to become aroused, it's a big part of the reason we start to dress up in feminine clothes in the first place, and one of our lasting joys.

As for technical advice...it's pretty simple to just pull your panties down a little, cup your balls through that delightful lacy fabric and just come on your belly or into your hand or a sock or...hell, the list of methods is endless. Don't be silly.

As far as feeling shame after your orgasm goes away; it's a normal problem too, and quite easy to understand. You actually felt a little weird about wearing them in the first place, but the thrill and rush of wearing them was the stronger feeling, so you didn't think about or notice much your awkwardness and shame until your arousal went away.
Also, plenty of people have conflicting sexual feelings of ALL sorts and feel shame or awkwardness or even depression following orgasm.

If you can afford it, I'd advise a therapist if it'd very important to you to keep doing this ( and it probably is)
Also, realize there are many males who feel exactly the same as you do.
Think about how you feel about people who have different sexual needs than you do. Do you think they're weird or sick? Or do you just think they're different, and why not live and let live? They're not hurting ANYONE.
You probably feel the latter (at least I hope you do). so give yourself the same kindness and tolerance you give others.

Also, share your feelings with others (and you've taken a good first step here). Taking the courageous step of sharing it with those who love you and are closest to you will help a GREAT deal.

And, for the rest, it's just going to be time and living your life and learning and growing, sweetie. Like we all do. No one can really solve your problems but you, but share and get support, and you will. ^_^

And finally ( and really, I'm not being mean, truly) STOP BEING SUCH A DRAMA QUEEN! if you cum in your panties, or get a pee stain, or a skid mark, or WHATEVER....just take them off and throw them in the sink and wash them, like any other girl. Silly Goose! ^_^

Hugs