First and foremost, you NEED to talk to your doctor about this. I understand your concern about medication BUT hormones that are unbalanced and making you feel the way you are feeling can make you do unintentional harm to yourself or your baby. Women do not want to think terrible things will happen but they do and it's important to speak to your doctor A.S.A.P.
Yes, most women feel "baby blues" after giving birth. The crying spells are very normal. For most women, it doesn't last long but for others, the "blues" go much deeper and deep depression sets in. When I was pregnant with my 3rd child, I had this overwhelming feeling that I was going to die. Everyday I thanked God I was alive because I just "felt" like something terrible was going to happen to me. Luckily, sometime after the baby was born, the feeling of impending death went away. Every women experiences something different but it is all due to hormones.
As for joining a gym, you can go to your local Walmart and pick up an exercise DVD to work out at home. If the shape of your body is what is bothering you, you can change that with exercise right in the privacy of your own home.
Does your child have allergies? If she is being treated for allergies then you should speak to the pediatrician over your concern of taking her outside. Honestly speaking, fresh air would do both of you wonders.
Will the feelings go away? They may eventually go away on their own but you don't know when that may be. Can you envision feeling like this for 6 months or a year or longer? Talk to your Ob/Gyn. Do it today. These feelings can get worse over time without medication and medication doesn't necessarily mean it will be long term either.