|The tech guy told me the switch could cause the entire network to crash. Is that true?|
Yes, it's very true. You could easily cause a loop that shuts down part, or all of, the network.
The switch has no software and when I hooked it up I had internet on both computers for a month until the tech guy found out. Is he making a bigger deal than it really is?
No, he's not. If you knew anything at all about that network, or networking in general you'd know this.
First off, if you're not the IT guy, you have NO business plugging anything in anywhere without prior approval from the IT person/department.
It's a simple enough process to discuss your needs with the IT people before attempting to take matters into your own hands. Where I work, you would have been fired for what you did and escorted off the property immediately because you're not a member of the IT department.
What I find particularly offensive about this, and you, is, you don't know squat about the network and networking yet you seem to think you're smarter than the person(s) that manage and administer the aforementioned network. You thought it was ok to just do as you please. If you didn't get canned, you should thank the good Lord above for the reprieve because I can promise you, had you done something similar here, you would indeed have been fired immediately.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.