If by "Net" you actually mean entire area's network, then your subnet mask for it should be wider, because 18.104.22.168/24 doesn't include 22.214.171.124/24, 126.96.36.199/24 and 188.8.131.52/24. To include all these 3 networks, you subnet mask for the summary network should be at least a /22. Also, you say you model this in packet tracer, but say the switches are too expensive In packet tracer devices are free.
If you are trying to come up with a real life network design, then you need to start with gathering the actual requirements. It is ok to just say you will segregate teachers from students using VLANs and different IP address ranges, but what requirement does it really address? What application you are going to be running in your network is the criteria that should dictate its layout. You need to define what students will use their workstations for and what teachers are going to use them for. Then, I don't see any subnet allocated for servers. What applications are you going to have in your network? In terms of defining your IP addressing plan - that looks ok, although I would use private IP addresses instead of public ones. That's a bad practice to use public IPs in your LAN unless they are really registered to you and you are advertising them to Internet.
Complementing with a guide about VLANs in Campus Network Architecture