Weight loss with difficult 3 monther

My sweet 3 month old son is what my doctor calls a "high maintenance baby". I need to be near him often and I'm lucky if I get 20 mins to myself and those 20 mins are spent cleaning bottles or feeding the dog etc... I have gained a lot of weight from breastfeeding and I feel so unhealthy... I actually really want to exercise but I feel I only can when someone can watch the baby ... My husband gets home late and I'm exhausted and in pain by that time... baby goes to sleep late because we have to get in a late feeding...I get up at 3am to feed baby and am already getting so little sleep I can't see myself staying up at 3 to exercise because my husband leaves at that time so I'm back in the same predicament if baby wakes up. The two mornings my husband is home I do workout but that's not nearly enough. I am eating healthy so exercise is the missing element. I do have time a few days in the afternoon but I can't just let him sit there and scream for 30 minutes so I can work out... he has terrible reflux and gas and the screaming makes it worse. It's seriously terrible just when I take a shower to hear him scream and watch him scratch his face. I give him a pacifier but of course it will fall out and then he screams louder because I'm on the shower and can't help. How do any of you with high maintenance babies work out?