There’s an easy way to figure out if you’re supposed to say “person and I” vs. “person and me.”
Say the sentence to yourself without the “person and” part. We know you get it right when you’re starting a sentence with just “I” or using “me” appropriately later on. There’s large swaths of the country that start sentences with “Me and him” but we know you wouldn’t do that.
“What works for DH and I” or “What works for DH and me”? Think to yourself “What works for I” or “What works for me”? Hopefully doing that has caused you to choose “What works for DH and me.”
Similarly when you’re labeling photos– “My BFF and I” would be appropriate if you finish the sentence “My BFF and I are eating ice cream” but is inappropriate if that’s all you’re labeling the picture with. Do you label pictures just “I”, or do you label them “me”? Therefore, the picture is labeled “My BFF and me.”
This has been a public service announcement from the grumpy grammarians.