If your family sent you low resolution (fuzzy, not lots of pixels) images, then there is nothing that you can do to improve the resolution. HEIC is not higher resolution or a better image than jpeg-- it's a smaller file and takes up less storage. The HE in HEIC is high efficiency storage.
You haven't said how they sent the picture. In Mac mail, you can choose the quality and size of an attached image with a menu selection like this:

On an iPhone you're given similar options when you choose to send it. Some email systems don't allow large pictures, and a couple of full sized images may not be allowed to be sent in an email. You may have to use a link to Dropbox or iCloud rather than email.