Hi there, I think you are doing great: eating right and working out. You should be proud of yourself. Most people in your shoes won't even workout as much as you do. Also, you shouldn't be ashamed to go to the gym, you know why, because most of those "skinny" people at the gym used to be plumb too at some time. I bet you they all felt the same. Besides, we all go the gym to get fit and stink it up. Just kidding. Also, I've noticed you bought a couple of fancy exercise stuff....well, use them at home especially if you're still uncomfortable with the gym.
Anyway, I know how you feel, I am going through the same thing. It's ok to plateau, everyone does. I know it's frustrating, but don't worry, be patient and believe in yourself. Try not to weigh yourself everyday, once or twice a week is ok. You might end up burning lots of body fat and gaining muscle mass. Also, try tape measuring parts of your body (arms, thighs, legs, waist, chest, etc), you will definitely notice a change there, even if you're weight's been steady. You probably never realized that your waist and thighs are a little slimmer these days.
I usually have fish (salmon, tuna, tilapia) and sometimes chicken for protein; and try to make all types of fruits and veggies your best friends.