Short answer, no.
Long answer, it depends on the situation.
But important – first rule of aria:
If you can use a native HTML element or attribute with the semantics and behavior you require already built in, instead of re-purposing an element and adding an ARIA role, state or property to make it accessible, then do so.
When in doubt, choose native HTML.
https://www.w3.org/TR/using-aria/#rule1
If you have a visible label, then you should connect the label text and the input field via the label-element.
If the input field does not have a visible label, the aria-label is one technique that can add the label semantically.
In your example of the button, you should use an aria-label, as the "X" doesn’t give the user any information. Of course, most users can guess what an "x" dos, but the user should not have to guess.
And here am talking of users who use assistive technology.
I would recement that you get a professional to test your site, for legal reasons but mostly for your users.
I'm a web developer, but have used the last 10 years on web accessibility. So far, it’s the hardest field of web development I hav had to learn and I'm still learning.