My switch is unmanaged too. That's not the problem. Thank you for clarifying that it is a gigabit switch. How old is the computer? Inspect the make and model number and look up the specifications online. They usually are widely accessible. What's the maximum speed of that port? I ask because discount models or old model cut corners on price here and should be updated. Hopefully it's a desktop where you can easily switch the port out with a faster one.
Assuming that's not the problem, there are a few things that can affect the speed. The maximum speed link I gave below goes over that in detail so I won't do it here. For example if you go to a website that's being privately hosted that only pays for a hundred megabits a second, that's the most they are going to upload when interacting with that website. That website is the bottleneck. That's unusual these days but it's still possible.
Assuming it's not that, I would start with making sure that the computer software is fully up to date, and power cycling the Fiber Jack on the wall and the router. >>>
Additionally, inspect the desktop/laptop specifications. If the hardware is dated, its ethernet port could also be limiting the speed. Here is a resource to see the approximate dates of computers and the speed typically available on the computers from that era.