Is there a way to upgrade a 1080i tv to 1080p?

Answer 1

No, a TV that can only do 1080i (or 720p, or anything less than 1080p) cannot be upgraded to 1080p.

It is a matter of not enough resolution able to be displayed at a time. 1080i only displays every other line at a time, so has half the resolution as 1080p. It will display every other line, and then quickly switch and display every other line that was not displayed first. 1080p needs to be able to display all lines at once.

Answer 2

No, the TV's panels simply has not enough resolution.
But you don't have to. Unless you have a really big TV (more than 42") and true 1080p content - which is rare - you can't see the difference.