Not shifting won't switch into third gear?

Hello,

In order for the transmission to shift it will require certain amount of transmission fluid pressure. So, it is always a good idea to check the fluid level make sure it is correct and in good condition.
Also, if the transmission oil pump is weak it might not provide sufficient pressure and the transmission will have shifting issues.
This can also be due to faulty shift solenoid.

Take a look at this article, it covers the basics of automatic transmission issues:

https://www.2carpros.com/articles/automatic-transmission-problems

I have attached diagrams for your reference.

Please let me know if you have any questions.
Thank you.