Why does it take so long for my iPhone photos to get sent to my e-mail?

Lee,

All kinds of factors can affect the speed of email being sent and received. It might, as you speculate, probably minimize the delay if you mail the photos directly to yourself at the same account that you're sending from. However, there are other options that would likely be faster.

You can send the messages to yourself via the Messages app.

You can use Photostream: My Photo Stream - Apple Support

You can use a sharing service like iCloud or Dropbox.

Lee,

I guess I should have asked whether the computer at the receiving end is a Mac. If it is, then you can do this pretty easily within the Apple ecosystem by just using the Messages app: either open a new message, address it to yourself, and tap the camera icon to select the image(s) to send, or open the image(s) and use the Sharing (upward arrow) tool to select Messages. The system will push this through as fast as your connection allows.

If the computer is not a Mac, then we're outside the ecosystem and I have no idea what I'm talking about, vis-a-vis messages, texting et alia.

But if you're using end-to-end email, then I'd pick one account — say, j****@gmail.com — and use that to send and receive the photos, so there's only one remote server involved.