I really like plots where there are male characters struggling with having feelings for someone they feel they shouldn't (love interest is same sex or pretends to be) or they struggle with being the 3rd wheel. Anyone have any recommendations?

Examples:

Coffee Prince- Choi Han Gyul

You're Beautiful- Jeremy & Shin Woo

Hana Kimi- Nakatsu

Lie to Me- Hyun Sang Hee

Flower Boy Ramen Shop- Choi Kang Hyeok aka Pillar

You who came from the stars
spring waltz
padam padam
immortal classic
these have third wheel guys
Oh also lights and shadows but it might be too long for you. But the struggle is one of the themes
Some are main some are not , some get the girl some dont

49 Days
Summer's Desire
Devil Beside You
Moon that Embraces the Sun
Itazura Na Kiss
Goong
Sungkyunkwan Scandal
Heirs
Dream High
Feast of the Gods
Empress Ki
May Queen
Luerd Kattiya
Ho Goo's Love
I Love Lee Tae Ri
Juunen Saki mo Kimi ni Koishite
Love Sick: The Series
That Fool
Two Weddings and a Funeral
Take Care of the Young Lady
Tiamo Chocolate
Sweet Sweet Bodyguard
Smile, You 
One Well-Raised Daughter
The Master's Sun

I feel like these fit with your description, but there are also some who can't be together because of their social status or due to their age difference.
I Really Really Like You - the girl likes someone else - although she shouldn't - while the male lead likes her and is quite the third wheel. Also, eventually, the guy she likes has some feelings back but since he is married...
Let's Eat - both seasons, actually. He only realises his feelings when she is dating someone else already.
I Need Romance 2 - mostly a 3rd wheel thing but it's also him thinking they shouldn't be together because of his "secret" (and that's why they're exes)
Witch Yoo Hee - he is dating someone else already
Valid Love - she's married and having an affair

Also there are plenty of noona romances where the male lead is not considered marriage material (too poor, too young), so to say, and thus in some sense "shouldn't" have feelings for her. E.g. Witch's Romance.
oh my goodness so many choices... thanks guys! 

I just love that moment of the guy looking at his love interest and you can just tell that his heart is in pieces. I'm not a sadist (I swear!) but I just love the angst soo much!
Hotel King - but it's vice versa, the male lead falls for the female lead even though he shouldn't (because he thinks they're related but they're not xD)
The Rose fits the bill. Kui is a very conflicted character who has feelings for his brother & for the female lead. Kui is the best thing about the Drama.
Cinderella's sister
Pin to Kona
Shut up: Flower boy band
Tatta Hitotsu no Koi
and there's one that's airing right now called ''Scholar who walks the night''. He keeps saying he can't have her because he's a vampire (she doesn't know). It's surprisingly good!