Can I replace my macbook 13 inch screen with another Macbook screen from the same year?

Depending on the version or build model/year of your MacBook the complexity of such an operation may be moderately difficult especially if you have limited experience or skills, and damages to other components that need to be disconnected/removed may result in the process.

(in short maybe Yes, you could; but maybe you shouldn't. the tech you spoke to may be wrong in their position)

A quick look through such sites as iFixit.com and a few others suggest there are several parts that could play a role in a portable Mac that has a display that winks out as the lid is moved up or down. I have an early MacBook first edition that sometimes does that; I leave mine in a open-position on a laptop stand so it seldom moves.

However there are parts that can be relatively easy to replace by an expert. For mine, I contacted a repair company of my previous acquaintance who fixed an older iBook (they do work to a high quality) that needed a similar repair, and they said my MacBook could be repaired. The company I had do this by mail, & was sent to SC in a padded box (priority mail/insured) -- said they could also fix my MacBook with an issue such as yours. A fair deal for me.

This was wegenermedia.com who did a good job and at significant saving over other more local companies who probably would've sent it to another repair shop out of state instead of actually doing the work themselves. You can email such a company via their site. I have no affiliation with them except for word-of-mouth and one repair done with good satisfaction. They can do under-warranty repairs, too; on those kinds of things that perhaps would not be covered (dropping) under AppleCare, so the remainder of the coverage would not be void, in a newer computer; for example of when a specialist can be best overall.

Hopefully this helps...

Good luck & happy computing! 🙂