Hi Amber and
to the forums!
Congratulations on your little boys! They sound adorable
As for the "screaming matches", that is perfectly normal and doesn't usually indicate an argument at all; the loud calling and cackling back and forth can often be to indicate an excitement to see the other bird.
It's most likely that they will get on just fine when you do put them together!
For now, I'd continue to leave their cages together; that's a great way to introduce them!
When you feel it's time they should meet face-to-face, it should be in a neutral territory (out of the cage or in a cage that is large enough for the two of them and has been rearranged if one of the budgies has already been living there to prevent territorial tendencies).
We'd love to meet your troublemakers when you get a chance!
Meanwhile, be sure to read through the forum's many articles and "stickies" (threads "stuck" to the top of each subforum for easy reference) to ensure you're up to date on the very best of budgie care.