This TV show aired on Saturday night, August 19th. It might have been on
Nick at Nite at around 11 or so, but most likely did not (I looked
into Nick at Nite schedules for that night and couldn't find it
myself).

One guy (who is running for student council president) wants to give
the other a picture they took in a photo booth (it's of him kissing
the other guy on the cheek), but the other guy doesn't want it because
he's afraid they'll get caught.

The end result is that the first guy tells his mom he is having
relationship problems - at first he denies he's gay, but then he
admits it and breaks down.

What is the episode title and title of the show it appeared on?

I believe your show is an episode of "Degrassi: The Next Generation."
The episode's title is "King of Pain." It has been aired several times
this month on a cable channel called "The N" (AKA "Noggin").

"Marco is taking pictures in a photo booth for his student council
election poster at the store where his Mom works and Dylan kisses him
in the fourth picture. Marco starts getting worried that his mom might
have seen them. He rips off the picture with him and Dylan and gives
his Mom three pictures, leaving his Mom suspicious."

TV.com: Degrassi: The Next Generation: King of Pain Recap
http://www.tv.com/degrassi-the-next-generation/king-of-pain/episode/317064/recap.html

"Marco is inside a picture booth, posing unenthusiastically... Marco
makes it through three poses, grimacing after each one, before Dylan
pops his head through the curtain and gives his boy a kiss on the
cheek... Marco is not thrilled at the semi-public display of
affection. As it turns out, the photo booth resides in the drugstore
where Marco's mom works... The photos are for Marco's campaign posters
- he's running for president of Degrassi's student government."

PopGurls: Degrassi S4: King of Pain
http://www.popgurls.com/article_show.php3?id=505

"Marco, running for student council president in the upcoming
election, sits in a photo booth posing for pictures. His father, a
printer, plans to create a poster for the campaign. Marco's mom works
in the store with the photo booth, and Marco's parents do not know
that Marco is gay. Marco is rattled when Dylan, Marco's boyfriend,
pastes a kiss on Marco's cheek that is captured on film. When Marco's
mom asks about the photos, Marco hides the one of him and Dylan. Dylan
later tells Marco that he is tired of pretending that he and Marco are
just friends. Marco, who expected to run for president unopposed,
discovers that Alex is also running. With Dylan about to break up with
him, and Alex posing a serious challenge, Marco is clearly upset. When
Marco's mother asks what is wrong, Marco says he's having
'relationship problems.' As his mother questions further, a teary
Marco finally tells his mother that he is gay."

The N: Degrassi: King of Pain
http://discussions.the-n.com/guides/summary.php?show=degrassi&ep_number=403

My Google search strategy:

Google Web Search: kiss OR kissing cheek "student council" "photo booth"
://www.google.com/search?hl=en&q=kiss+OR+kissing+cheek+%22student+council%22+%22photo+booth%22

Google Web Search: degrassi "king of pain"
://www.google.com/search?hl=en&q=degrassi+%22king+of+pain%22

I hope this is the right show! If it is not, or if anything is unclear
or incomplete, please request clarification; I'll be glad to offer
further assistance before you rate my answer.

Best regards,
pinkfreud