A similar thing happened to me several years ago....I thought I was in good health, but suddenly became constipated. Nothing worked, and it was very odd because I never had any issues. I was new to enema's, but they gave no relief. I tried colonics, and was told it could take several sessions to clear a blockage if that is what it was. I had just had a CT scan at the ER which showed no blockage. The colonic therapist had not seen this either, but recommended raw garlic for the bloat until we got it figured out. On the third day of raw garlic, I passed a bundle of worms. I knew nothing of parasites at this time.
It's possible that juicing has stirred them up, they ball up in defense mode, and also release chemicals to slow your bowels down. I would definately look into parasites as a possible reason for your problems.