Feeling so despondent

With my first son, I gained about 70 pounds. I lost all of them, mostly through yoga, walking, and carrying my son in a backpack. The last 25 pounds I lost, I did with a formal diet, which worked, but was a pain to track the way the diet wanted you to track your food. It took me about 18 months to lose the weight, the last 25 were in the last 12 weeks of that time period. With my second son, I didn't gain as much, but I was so tired all of the time, I didn't have the time or the energy to do what needed to be done to lose the weight. And due to some life happenings, I have gained more over the years; my current goal is to tackle getting rid of some, if not all, of it.
So here are some thoughts...
If you need the calories for your baby, then exercise is probably where you need to concentrate for a bit.
Yoga can be helpful. There are versions that are mom and baby together.
If you don't have a backpack to carry your son, try and get one. Then just walk some every day, carrying him in the backpack...my son loved his...he could see better what was going on. I would walk around the neighborhood carrying him, or on messy days, just around the house. Those extra pounds will build up your leg muscles some, making it easier to walk when you aren't carrying him. Pushing a stroller on walks works too, but not as rapidly.
If you can't do the baby backpack, try putting some cans of food in a small school backpack and wear that while doing things. I did this after my first kid, and it did help.
If you don't need the calories for your baby, check the diabetic food exchanges. There is very little that cannot be had, it's just a question of how much. Not sure how much access you have to a nutritionist, but meeting with one might be helpful. You might also try adding B vitamins and foods that have a lot of B vitamins...those are the anti-stress, anti-depression vitamins.
Are you eating to compensate for having to stay awake?, or not sleeping deeply enough to be truly rested?, and thus not getting enough good sleep? Been there, done both of those, was not pretty. Only real solution is to sleep uninterrupted by anything, preferably somewhere where household chores don't scream at you as soon as you wake up, and with confidence that someone else has baby duty. Say a weekend away with SO or by yourself.
There are also some facebook pages that are for new mom's to share and ask questions for help.
Hope some of this gives you ideas about solutions that fit into your life and schedule.

Its really simple although I know it might not seem that way..

If you have been using MFP for a month and your weight has increased, this means that you not adhering to your calorie deficit to lose weight.

MFP auto generates your calorie deficit (recommendation is to do 1 lb/week rate of loss) so just just meet your daily goal every day (do not go over and certainly never eat below it)... You will want to buy a food scale to weigh your food intake and log that in your diary. This is the best and only way to know how much you are consuming to stay on point with your diet.

This content has been removed.

One thing I'd ask, are you on any form of birth control now that the baby is born that can cause weight gain? My daughter in law was using some needle or something and gained a ton of weight after having the baby, sounding similar to you, heavier when my grand daughter was a year old then when she was born. Then her mother talked her into switching to a different form of birth control after reading a side effect of what she was using was weight gain and magically she dropped after switching, not quite to pre baby weight but certainly to a healthy weight.
Other than that, try not to worry about the scale, stick to your plan if you are logging properly and sometimes it just takes time. I've been low carb and low calorie for this entire month. I have tracked food for years on a different site and track my nutrition so I know i track accurately. So for some reason this time (different from past) i went up in the first two weeks a couple pounds, brought them down and finally after 30 days in the last week I finally dropped 5 lbs I was hoping to drop. Seriously discouraging so I remind myself that all that exercise and diet is about feeling healthier, increasing my stamina for the coming ski season, and not the number on the scale. I often find it can take me 5 or 6 weeks to determine if a weight loss regime is working with hormones, muscle inflamation and water weight fluctuating like it does. I try to record my highest weight and lowest and hope they are both trending down and tell myself not to get frustrated unless i see a number over my highest recorded weight. A mind set of if it's not going up and I'm following the plan and recording everything it'll kick in eventually.

And remember that even 2 lbs in a month, though slow, is 24 lbs at the end of the year. Breathe, find fun activities with the baby that you enjoy and help you.