Assalaamu alaykum sister,
Ramadan is not easy, is it? If you really feel like it's too much strain to fast while nursing, maybe wait until next year sis! I really do love Ramadan but it's like spiritual boot camp, and it's easy to feel demoralized.
Like many Muslims, I feel like I drift from feeling spiritually elevated to having very low iman. And when I look at my life, it usually comes back to how much am I trying to live the deen. If I am trying to pray all my prayers with kushu, if I am trying to pray extra prayers and do dhikr when possible, if I am really trying to be mindful of my actions and especially my tongue, I have a better time with deen. If I slack and gossip/backbite, if I watch too much TV, if I let my temper get the best of me with my daughter, etc., I feel further from my center.
The best Ramadan I have had (and bear in mind this is only my fifth fasting) was right before our daughter was conceived. I prayed Tahajud every night and gave myself a lot of time for sehri, then stayed up after Fajr and listened to my husband read Qur'an (I couldn't read it then.) And I was careful about completing my Taraweeh every night with concentration.
Having kids throws a monkey wrench into things. We are told that family is a fitnah (this is in hadith but I can't tell you the source right now.) I used to find that idea offensive but I understand it now. As wonderful as parenting is and marriage, they both take your focus off your spiritual life in some ways. As a mother, I have to pray with my little one right there trying to get all my attention and even trying to take my hijab off constantly some days!
And I'm up all night sometimes and have a hard time getting up for Fajr.
Anyway, sis, take the exemption if you feel it's too hard on your health to continue. I am concerned if you're still feeling super run-down. I'm somewhat hypoglycemic but was feeling OK with the fasting after a few days' time. InshaAllah search your heart and remember that while the imam is right, nursing/pregnant women are supposed to fast in OK circumstances, he neglected to mention there's a very well-deserved exemption for those who can't do it. I fasted with a one-year-old who still loved her milk and I might not do it again, or I might do every other day in that circumstance. I wish you a blessed Ramadan and I'm sorry you're dealing with this frustration.