Steam only downloads after I've paused it

In Preferences->Downloads there's a number of options which could cause your problem. The two most obvious are...

• Switching to a different mirror.
• Removing a bandwidth limit.

Try a large download from another site outside your school's network, perhaps another game utility. For example, does Origin or Glyph have the same problem? If they do this would indicate it's not Steam but something about your computer or network.

You should also check your total throughput of your connection using a site like speedtest.net. Be careful to note the difference between Mbit/s (megabits per second) and Mbyte/s (megabytes per second). Speedtest, and most ISPs, will report in megabits. Everyone else uses megabytes. 8 Mbits == 1 Mbyte.

Check if Steam is being blocked or throttled by a firewall or anti-virus, either on your computer or on your router. Conversely the problem could be a virus; if you don't have an anti-virus, get one.

If you're on wifi, try a wired connection. This will avoid interference from various sources.

Finally, the behavior you mention where it starts fast and then slows down is common among some shady ISPs (and some big ISPs are shady). This lets small downloads happen fast, but large file downloads get throttled. Web pages are made up of lots of small files, so they load fast. This lets most users have a responsive experience, but penalizes people downloading large files (and thus using a lot of bandwidth).