Going from 1 child to two was the hardest transition I have made. Take it easy on yourself! I was so exhausted for probably the first 6 months that I would literally forget what I was doing while in the middle of doing something. It will get better.
The baby weight will come off gradually. If you are nursing, you need to rest, don't worry too much about clothes fitting for awhile. It took me a year with each of mine before I was back to pre pregnancy size and this was with lots of work. You do need that bit of tummy until you are finished with nursing!
If it makes you feel better try and go out with a female friend or relative and buy some clothes that fit you now, just don't spend a ton on them. Or, if you plan on having a third child someday, go ahead and spend because you will get to use them again (this is what I did anyway).
Once you have caught up on sleep (a bit) and have a routine going it wil be easier to take them both out. It really did take me a couple weeks to get the hang of it (getting them ready & OUT at the same time was the hardest part), but with DS3 it was old hat--no problem--from the start!
Take care 