Do you have cholesterol problems if you don't eat any cholesterol? Why?

Many Considerations. See your physician. The first step is to determine why your lipid values are abnormal. Several inherited and acquired medical conditions (thyroid problems, high glucose, kidney disease, etc.) will affect lipid levels. If related conditions are identified it is appropriate to treat those while also starting diet, exercise and lifestyle modifications.
Body makes. Cholesterol as part of the normal metabolism. Cholesterol, despite its bad reputation, is needed for normal health. You need to get you blood lipids tested in fasting state to find you if you have a "cholesterol problem".