OP this is normal, it happens to everyone at 3 months and does NOT mean your supply is dropping. What it does mean is you are switching from hormone driven, post-birth supply to normal, established, demand-based supply.
Between feeds, your boobs will stop feeling "full" and feel floppy, soft and "empty". This is okay. Milk doesn't get stored between feeds anyway, it is made as and when the baby needs it. It's only that in the first 3 months your body isn't sure how many babies you've had, so it goes a bit mad and produces milk all the time. You will probably find that if you miss a feed for any reason then you will feel engorged again. That doesn't mean you should feel engorged every time.
If you have been expressing, your output up to this point might have been quite a lot - it will now have dropped to a more normal amount of only getting 30-40mls per pumping session. This is because a baby is more efficient than a pump, a pump is really only effective when you have a lot of milk "waiting" (which happens sometimes when the boobs get a bit overenthusiastic!) or if you're lucky - some people seem to be prize milk producers for the pump.
You'll probably stop leaking so much - again because your body has calmed down and gone "Okay - we know how much this one wants now. No need to panic and produce it all the time any more."
You are right that if you want to get your supply up then you need to feed as much as possible. Remember, milk is made on demand, so if she is latched on, there is milk coming. You can switch breasts as many times as you like, offer both sides and then the first again, you can offer 4, 5, 6 (+!) "sides" per feed with no problem.
I agree also, it is normal for them to suddenly become fussy at 3 months and seem unsettled for no reason. Ever heard of 3 month colic? A lot of babies also seem to want to be held but only when you're standing up. A sleep regression/growth spurt is normal too - she might be gearing up to rolling, sleep "blips" are usually related to developmental spurts. Or, it's not too early for teething to have started, it starts months before the teeth actually appear.
Good luck! And don't worry - you sound like you're doing fine :) Give your DH a if he dares make any digs at you.