Blue is the one colour note that can skip past gold or silver logic entirely, because it isn't trying to match your metals, it's trying to match your clothes. Before anything else, think about which blue you actually wear. Navy, denim, cobalt, a washed out chambray, they all read as "blue" on a product photo but sit completely differently against your skin and your clothes, so picture the two or three things you'd actually wear them with before you buy.
Fit wise, earrings live or die on the back and the drop, not the colour, so don't let a nice shade distract you from the basics. Check what fastening is behind the stone or bead, a lot of the cheaper coloured pieces use a cheap alloy post that a surprising number of people react to, especially on a second hole. If you've got sensitive ears, look for anything that states it's nickel free or has a surgical steel post, because a lovely blue drop sitting in an angry pink earlobe is not the look. Weight matters too, a big glass or resin stone can drag a stretched hole down by the end of a day, so if you're prone to that, go for a stud or a short drop rather than anything that swings. And hold them against your actual hair colour and skin tone before committing, a blue that looks brilliant on a model with pale skin and dark hair can go slightly flat or muddy on someone with warmer colouring, which is the sort of thing you only find out after you've already cut the tag off.
If you own none, start with a small navy or dark sapphire-toned stud, nothing bright or novelty. A dark blue stud reads almost like a neutral, it goes with black, grey, camel and most denim without ever looking like it's trying to coordinate with your top. Save the louder cobalt or turquoise pieces for once you know you actually wear colour near your face, because that's a different commitment to a safe navy dot. The dark stud earns its place in daily rotation precisely because nobody clocks it as "an earring choice", it just looks finished.
Occasion wise, blue earrings are oddly good at bridging seasons. A pale or chambray blue pair feels right from spring through to early autumn, worn with white shirts, stripes, linen, anything a bit coastal. Darker, jewel toned blues come into their own from autumn into winter, next to black polo necks, grey coats and that one good navy dress everyone has. They're an easy choice for work, for a Sunday lunch, for anything where you want a bit of colour without putting on a statement necklace and a personality to match.
If the post sits loose or tilts forward when you put weight on it, that's the wrong size hole for the piece, not a fault with your ears.