Not at all, trying to hard is often in the eyes of the beholder; people that don't really have much of an interest in or actual knowledge of fashion and style will consider almost anything above their norm as trying too hard. You can of course go to extremes, such as the example you described, but then it would me more weird than a case of the try hards.
You obviously have to be situation appropriate, take into consider the setting, company and purpose and tailor an outfit to suit but you should still remain comfortable in it. Anyone whose opinion actually matters will appreciate the way you dress for what it is and will probably compliment you for it, those accusing you of trying too hard are pretty inconsequential beings.
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