For our 16m/o, a "No child, none of that" in a disapproving but not angry tone, as often as necessary, gets the point across; while we aren't ignoring her, what she's doing for attention is not kosher. If she persists, it's usually because:
- she's bored (this seems to be your child's primary complaint, as a change of scenery does the trick; maybe you can step away from your other duties for a little while and indulge her),
- she's hungry (offering her an animal cracker is a good gauge; if she wolfs it down we get out something more substantive for a snack or meal, while if she plays around with it it's boredom), or
- it's naptime (there will be other signs like droopy eyelids, face rubbing, and the fact that when we lay her down in the crib she doesn't argue the point).
You might be tempted to try Pavlovian methods here; reward the good, ignore the bad. This is IMO a mistake; your daughter is trying, in her own way, to make sure you still have her back, and to ignore that can be damaging. It can also lead to escalation to a behavior you cannot ignore, which will reinforce this path of behavior as something that will eventually get your attention.
You should be responsive to your child. If this behavior seems engineered to get a particular response (she has, for instance, learned that whining will get her picked up and maybe even carried outside), then break that cause-effect relationship by consistently providing a different response to that behavior that she doesn't want (it doesn't have to be a punishment per se), and encouraging a different behavior that will get her what she does want (if that's within your power).
Just don't be too responsive; there are parents who take the exact opposite tack and respond earnestly to every movement and sound their child makes. First, this is impossible to keep up, and second, if you are always watching your child, they get the impression that something's up and maybe they're not as safe as they think.
By the same token, don't ignore destructive or overly disruptive behavior. As a parent, listening to whining is in your job description (Section II, Paragraph 3, right next to "being indispensable one moment and an embarrassment the next"). However, if she escalates, respond, this time with a firm "no" and/or a time-out.
The whining, the wanting to be held, the wanting Mommy (or Daddy) around all the time, is all part and parcel of the "clingy phase" that happens around this time. As babies learn to walk, run, climb, and generally push the envelope toward independence, they're also redefining their "comfort zone", and sometimes that will involve a regression or two back to "mommy needs to be with me all the time or I don't feel safe". Your child will outgrow this. In the meantime, giving her a response, but not the result she was after, is the order of the day for behavior you want to discourage.