Feels like I need to pee all the time? But no fever and no actual pain.

UTI? As suggested in your question, your symptom can still represent a uti. Other several possibilities includes-1. Diabetes (though other symptoms would be present) 2. Environmental irritant (soap is too alkali or irritating) 3. Anatomical issues (retention of urine) or 4. Physiologic problem (overactive bladder).