Your plea for help is noted. I hate to see a lady in pain. But what can I, a mere public servant in Guyspeak County, do? My hands are tied, but I will do my best to aid you from afar.

Strengthen that core. Some of your desperate cry for help may be from sheer laziness. Sorry, but FG don't play, sometimes. The fact that your boobs are difficult to carry is a simple issue of body mechanics and balance. Pilates, yoga and other core strength exercising will give you the lumbar strength and foundation you need to more effortlessly transport your breasts.

Get a better supporting bra. Don't compromise function for form. Not all those Victoria's Secret bras are meant to be worn every day, especially the ones that are ¼ the size they should be. Break out your heavy-duty, under-wire bra, the one you usually reserve for cleaning the apartment and start rocking that one every day.
 
Breast reduction. Though costly and invasive, if you have tried all other things and still can't lug your boobs out of bed, is an option. Go to a doc and see what can be done. If money is the main problem go online, there's probably a scholarship or chest fund out there for this exact dilemma.
 
Deal with it. Most people don't like the bodies they have But seriously, we are a picky, finicky,  'I want what she has' society.  Bring me ten women and I'll show you ten women who want different boobs, actually nine, there's always one that has a perfect set of breasts.  The same is true for guys, with their calves. But the point is, you may need to accept and learn to manage what the universe and genetics have betrothed to you.
 
Am I happy I have washboard abs, a jaw droppingly large penis and perfect bottom teeth?  No, of course not, but I deal, and perhaps, so can you.