I have a 33-month-old and a ten-month-old. The older of the two has been very whiny lately, constantly wanting to be held. My younger child is teething and is also very whiny, but I think has a valid reason. The older one has all her teeth, but still insists that her teeth hurt, especially if the younger one is getting medicine. What is going on?
There are many reasons why toddlers and preschoolers whine (and they can be notorious whiners at this age!)--boredom, fatigue, stress, jealousy. For your situation, I agree with your hunch that it's probably not your daughter's teeth that hurt, it's that she sees you busy with the needs of your younger one and she wants your attention as well. I'd guess the rough translation of her whine to be "Don't forget me, I need your attention, too.."
Hopefully, you have time in your day to devote exclusively to your toddler. This may only be a half hour, maybe as your infant sleeps or someone else cares for him or her, but time that you and she can look forward to and plan together. This one-on-one time is often a boost for both parent and child.
Another strategy is to incorporate her into your chores as the 'older one', the helper, to keep her busy and to make her feel an important and included part of your day.
If neither of these suggestions work, try to pinpoint her whiniest time of day, to hopefully figure out what events are triggering her emotions or the source of her frustration.