This is not about me, about my need to be right or my pride or desire to show off or put people down or prove anything. It's also not about run-on sentences, so let's move on. The part that is me is the desire to respect our language and to understand it and to use it in a way that is both useful and graceful.
People have probably told you that, when speaking properly, you say "...and I" rather than "...and me." While that is sometimes correct, it does not apply to every time you want to add yourself as a participant in a sentence.
As bad as "and me" sounds to the people who told you, "it's 'and I'!", that's how bad an incorrect "and I" sounds to the discerning ear. In fact, it's a little worse, because it sounds like the person is trying to speak properly and, in doing so, is drawing attention to the impropriety of it. I'm not mad at you. I'm mad at the people who tell you "it's 'and I!'" without giving you the full story.
If you say, "Glen and I went to the Viper Room," that is correct. "Glen and me" would not be.
However, if you say "There were all kinds of people at the Viper Room, including Glen and me" then saying "...and I" would be incorrect.
The difference is that you say "and I" when it's before the verb of the sentence. In the first example above, the verb "went" comes after the names, so it's "Glen and I."
You would correctly use "and me" if it comes after the verb of the sentence. In the second example, "were" acts as the verb, and the names come after it, so among the people "were...Glen and me."
The easiest way I've learned to remember the difference is that, if you remove the other name(s) from the sentence, and it's just you, would you say "I" or "me"? "I went to the Viper Room" sounds normal. "Me went to the Viper Room" sounds like Jar Jar Binks. In the singular example above "were" becomes "was" and it "was just me."
The key may be in determining what the verb of the sentence is. In the example "This is a photo of Glen and me" the verb is "is." That doesn't sound like much of an action word, but it's the only thing happening. It's sometimes called a linking verb. There is no other action in the sentence. Even if you add a verb after the names, such as "This is a photo of Glen and me posing for the camera" saying "and me" is still correct because "posing" is not THE verb of the sentence. Even with a 'real' verb such as "posing," "is" remains the verb of the sentence because "is" describes the photo, not the action in the photo. "Glen and I were posing" works, because the subject of the sentence is Glen and you, and posing is what you were doing. But if "photo" is the subject of the sentence, then "is" is the verb. Therefore, "This photo is of Glen and I" is incorrect, as it is a rare and likely archaic instance when you would end a sentence with "I".
It is I who thanks you for reading.