By me rupturing my ovarian cyst could that cause me to have constipation?

Usually not: It's more likely from the pain meds if you were given any. Narcotics are notorious for causing constipation (tylenol (acetaminophen) with codiene, vicoden, percocet, etc). A ruptured cyst often causes pain but should not affect your GI tract.

Not really: Pain associated with the ruptured ovarian cyst may warrant strong pain medications that may in turn make you constipated.