I can't figure out what I'm doing wrong?
The thing you have wrong is planning.
A designer needs to take into account the limitations of the medium, the usage, context, etc.
The logo needs to be an actual logo that works in different environments, with these limitations and characteristics.
Some variants need to be prepared, variants in colors, in positions, in arrangements, in the information displayed.
Also, the webpage needs to be adapted.
These are only some reasons for a logo to be constructed in other programs than PhotoDoNotUseItForThisShop.
If you are paying the adobe suite use illustrator if you want a free program use Inkscape.
But let me address one more important topic here. I am pretty sure you do not cut your own hair and make your own clothing. And you do not construct your own furniture, machinery, computers or whatever you have on your business. Someone else does them, so you can rely that they are the best looking stuff and the best quality you can afford.
Do that for your Logo, for your website. Give your business a chance to look good. This little problem with a blurry logo is just the tip of the iceberg.