option to hide giveaways we have already entered?

That might be an option with the ESGST extension, but I'm not sure. I'd recommend installing that extension regardless if you don't already have it since it makes browsing this site easier.

ESGST can help you with that.

I see that you joined a week back, Im a newcomer myself. You should take the opportunity to further explore the site.
If you look at the right side column, the first option is Add-ons/Tools. Where you find further details about ESGST.

Here's a simple userscript:

// ==UserScript==
// @name         SteamGifts - Hide Entered Giveaways
// @description  Hide giveaways already entered
// @namespace    https://www.steamgifts.com/user/ormax3
// @author       ormax3
// @match        https://www.steamgifts.com/
// @match        https://www.steamgifts.com/giveaways/search*
// @icon         https://cdn.steamgifts.com/img/favicon.ico
// ==/UserScript==

document.querySelectorAll('.is-faded').forEach(el => el.parentNode.remove());

Or you can create it as a bookmarklet if you prefer:

javascript:(function(){document.querySelectorAll('.is-faded').forEach(el => el.parentNode.remove());})()