Agree with above advice. My 2yo dd went through an incredibly picky phase a few months ago and I just kept offering her everything and taking it away if she didn't want it.
I once found myself thinking in utter frustration, 'For god's sake, she can't live on bananas, porridege, yoghurt and bre... Oh, actually, yes, she can!'
If she sees you're anxious over it, it will become a way for her to exert control in a negative way, and let's face it, toddlers don't have much control over their lives. I think the only answer is to keep persevering with offering her a wide variety of foods.
With dd, I would prepare whatever we were eating, offer her some of that, and if she really didn't want it the options were yoghurt, fruit or toast, not an alternative meal. In the last couple of months her eating has improved hugely, I just think the only thing that works is time and patience - and sometimes seeing other children eating, too.
Sorry, I hope all this doesn't sound like a rant - I feel really strongly about this, because I ate hardly anything as a small child (not picky with what I ate, just tiny quantities) and my parents were very patient and calm about it, and now I eat like a horse. I just dread to think what would have happened if they'd forced me to eat more.