Hey i know how you feel.
I have a 3 yo boy and 9 month old girl...so i always feel a little tired at least.
Usually i feel like that when i hate my body...i figure i look like cr*p so i dont motivate myself to do anything.
I understand the catch 22 part because when i exercise i love the changes in my body but when i dont i let myself get down even though i know i
should be doing something.
Usually it is just excuses and in your mind they are perfectly justified.
I can guarantee that exercise and eating well will give you more energy and help boost you throughout the day.
Take the opportunity to relax any chance you can get...when ur baby is sleeping or playing on her own.
Also what i usually do is set one day of the week...cook and freeze the meals that i need during the week...so i have little preparation to do during the rest of the week. Make sure you have healthy snacks only in the house so that when u get hungry...thats all there is...my favorite is low fat yoghurt.
Good luck and i hope ur feeling better soon....its just a matter of starting....no excuses!
