For me, melodrama = fake, and "melodramatic" is not necessarily the same as highly dramatized. If something emotional or actiony seems fake, out of character, or off-tone, then it will get that dreaded "melodramatic" tag. But there isn't any sort of red line, it's all contextual. If you have a teen character, for example, they are probably going to over dramatize things occasionally, but if it reads as a genuine act then it still won't be "melodramatic" it will be melodramatic in the way teens actually are.
"Romeo, Romeo, where for art thou Romeo" all by itself sounds pretty "melodramatic", but if you read the whole play or watch it performed it works in context. It doesn't feel fake or like a mockery or an overreaction. I just read a Pratchett book (yeah still reading them) and a guy starts slaughtering a mob of dwarfs all by himself while screaming lines from the toddler book "Where's my cow?" (or something) and yet it wasn't "melodramatic" because it's a work of satire and comedy. It was goofy and over the top, but as part of the climax for an already light-hearted book, it was fine. It fit the moment, and there were previous elements that fully supported that reaction.
I went and looked up the actual definition of melodrama, and I think it backs up my interpretation.
Melodrama: "...exaggerates emotion and emphasizes plot or action at the expense of characterization."
I think the word melodramatic actually has a couple meanings with small but significant differences, and that makes it a word that can cause a lot of confusion depending on how people interpret it. Overly dramatic or sensationalized is not quite the same as "like a melodrama." What some people call melodramatic might just be someone acting out of character, or an indication that something wasn't indicated well enough earlier for readers (but you as the author understood the relevant minutiae of the backstory better).
So I'd say as long as you aren't abusing your characters and making them do things for the sake of plot or trying to generate a reader reaction regardless of how the character would actually act, then it's fine. Some people or events are more dramatic than others, but make sure they are justifiably so for the reader. Someone cowering under the kitchen table and biting their nails during a thunderstorm might seem "melodramatic" at first glance, but what if it was previously established that they had an intense fear of lightning due to a past experience, or were mentally disabled and afraid of loud noises? Then they're simply being scared.
Edit: After looking around a bit, I think it is pretty clear that the current common conception of a melodrama does not match the historic one. It's basically been dumbed down to just "very dramatic." Tons of character-centric stuff gets labeled as melodrama now.