Hmm. I'm tentatively assuming that what's burning your nose is either aldehydes or an excess of musk, so I'm keeping that in mind in the recommendations below. I should make a point of saying that I wouldn't recommend buying anything unsniffed.
My first thought for a line that has a variety of high-quality, fairly complex fragrances available in that price range is Annick Goutal. They'd only be in your price range at discounters, but there are perfectly reliable discounters, like BeautyEncounter. (Or Amazon, if you're more comfortable with them.) BeautyEncounter sells samples, too.
Another possibility is the Jo Malone line, though they break your price boundary slightly - the 30ml bottles are $55, and I've never seen them discounted. My favorite by far is White Jasmine & Mint, but Sweet Lime & Cedar also seems to be very well regarded.
The Elizabeth W line might be too plain for you, since you mention complexity - it's mostly straightforward florals. But you could try the Sweet Tea, if you can get your hands on a tester or sample. Tea, lemon, almond honey - it's very nice, and very inexpensive. And the Rose is a lovely simple rose. And I love the Magnolia. And now that I like tuberose I'll be trying the Tuberose again...
Specific fragrances that are widely available at a good price from the discounters include:
Bvlgari Black is a nice vanilla/tea/rubber fragrance, and don't let the word rubber scare you - it really is very nice, definitely worth trying.
Many people adore Rochas Tocade, a rose and vanilla fragrance. I don't get it myself, but you might love it as much as they do.
I do love Balmain Ivoire, a rather stern green and soapy fragrance - even though I usually hate soap.
Balmain Vent Vert is a shadow of its vintage self, but if you never smelled the vintage, the modern version does smell pretty darn nice.
And in general, just go sniff. Sniff everything, even if the price tag is impossible - once you know that you love a given fragrance, people might be able to recommend something with similar notes that's less impossibly priced.