I'll just file myself in under here and agree that contrary to the wave of "just try harder!" and "try this other thing!" comments that came in reply, that going in to an exercise program and finding that it makes your life
worse is quite possibly the sign of a serious medical problem.
I'm actually in that boat right now. For the last few years I have struggled with an exercise program on and off. I have consistently had the experience that it initially makes me feel better, but then I hit a plateau of a certain level of progress that makes me increasingly tired as I try to "push through" and prone to getting every cold that wanders by. Well... guess who's typing this while wearing a heart monitor for a month? My diagnosis is not yet complete but at this point I'm fairly confident I have a condition where my heart goes into some serious atrial fibrillation, only while I am asleep [1], resulting in me not being aware that I may have a moderately-serious heart condition probably for quite a few years (quite possibly decades) until quite recently.
My point is not that you may have this exact problem I have. Delores12 is also correct that this is a known effect of Chronic Fatigue Syndrome, and as documented on HN that has recently been getting upgraded in the medical community from "ideopathic condition we're not sure we even believe in" to a real diagnosis with a real mechanism, and there are other things this can indicate. My point is "exercise actually makes me feel worse" is a potentially serious symptom of something, and rather than feeling guilty about it or getting moralized at by people who do not have this experience, I would strongly suggest going to a doctor, getting a physical if you haven't already had one, and finding a doctor who takes this seriously as a symptom if the physical doesn't find anything immediately.
I wish I had gone to the doctor earlier. I have some other local health issues that mean that even now I can't actually say what I did was irrational per se, indeed I even found some other issues I had in the meantime, but now I'm in a position where my condition is sufficiently bad that I'm beginning to feel like I'm in some sort of sleep deprivation torture experiment some days, worse than when I was a new parent, and I'm not joking or exaggerating for effect. Unfortunately the medical system is hard to make move faster than it wants to. If you can find what your problem is before then, you'll be happier.
[1]: I do not need people to pop up with the possible causes of this; I am currently engaged with the medical system and aware of the possibilities related to apnea, etc. (I have recorded myself at night and I do not seem to have a snoring problem, so if it is apnea it's the relatively unusual, but existing, no-snoring version. It may also simply be genetic as my mother is prone to it.)