The transmission only has first, second, and reverse gears?

There is no way to put the transmission in third manually. It sounds like the shift solenoid is not working but can I ask if you have a check engine light on? If so, we need to see which codes are stored, this guide can help:

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Also, I would check the transmission fluid to see if it is burnt, the transmission might need to be rebuilt. Please go over this guide as well:

https://www.2carpros.com/articles/how-to-check-and-add-transmission-fluid

There are also 6 fuses that run the system I would check those as well, here is the transmission wiring diagrams which show which fuses to check, check out the images (below). Let us know what you find.