I know exactly how you are feeling Ishani, I went through it with each of 3 DC's, like others, after bf I ended up heavier than I was days after giving birth - I consciously allowed myself that time though, to eat whatever and take it easy exercise wise. It's not necessarily the best approach but I regarded it as time for me to make sure focus and energy was spent on the baby and not put extra demands on myself IYSWIM. I did try to stay well groomed and nicely dressed in (baggy) clothes though
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After I stopped feeding them I was almost sick of eating constantly and felt uncomfortable, so focussed each time on exercising. After DS1 was 9m I didn't diet, other than cutting back a few nights a week on wine, resisting the obvious cakes and choc and trying to avoid carbs after 5pm. What I did do was exercise hard and I lost nearly 2st over about a year. After DD I just started back exercising when she was 10m but got pregnant (unexpectedly) so started 2nd pg 1st overweight.
I stopped feeding DS2 in January, just after his 1st birthday and have been exercising almost every day since, also, I didn't want to take ages to lose the weight this time, just wanted to get back to weight/clothes/fitness I got to before DD quickly, so I also watched what I ate very carefully (I wasn't calorie counting as such but intake was maybe 1800 cals a day with 400 cals burned through gym) for 3 months during which time I lost 1.5st. I would still like to lose up to 1/2st more but I am a size 10 again and toned and I feel great. What kicked me into action? That sense of feeling uncomfortable in clothes, unfit, unattractive and so generally dissatisfied even though every other part of my life was great....the result of changing all that is more energy, a much better sex life (DH didn't criticise before but is definitely more attracted to the smaller version of me and I am more enthusiastic too now I don't feel self-conscious about being overweight
). My time exercising is also time for me and taking that every day makes a big difference psychologically, makes the relentlessness of looking after young DC's less so.
Is there really, really no time for exercise? Just 20 minutes a day? If not a gym with a creche then could you find a slot to get out and start walking/jogging (with DC's in buggy if necessary) but if not then doing a dvd such as Shred while DC's nap/play? Could you do a class like pushy mums in a local park? Do you have a friend in a similar situation that you could have each others DC's for half an hour each while you get out? You have to think of it as time for yourself, which is really important and an investment for all of your family - nobody benefits when you are feeling frumpy and fed up and conversely you will be much more fun when you have a bit more energy and feel better about yourself.
I firmly believe that if you start exercising and paying a bit of attention to hair/make up/nails, (even just making sure they are clean/cut/etc) then more interest in your body in terms of what you are sticking in it will follow...if you can commit to 20mins a day of something it will become a habit after a couple of months, you will see and feel the benefits and crave that space for yourself - you won't want to skip more than a day.