That makes no sense. Internet access by "hotspot" is a connection using an 802.11 (a/b/g/n) "wifi" connection. This is not to be confused with cell phone data which uses a 3G/4G etc. connection. True "wifi" is basically wireless Ethernet, although a lot of people do confuse the two. And when you connect to an open public "hotspot" like at a Starbucks or McDonalds then you should have no data caps or any other restrictions to worry about - "they" are paying for it! In fact, public hotspots are great for obtaining updates and any other downloads that don't contain sensitive information. However, public hotspots like that are almost always a bad idea if you need to do anything sensitive like online banking. (It's like trying to file your taxes by addressing it, putting a stamp on the envelope and then throwing it out in the street for anyone to pick up and hopefully deliver to the nearest mail box.)
Now, that's as far as your cell phone is concerned. But then you ask about your computer?! I can only guess that you are "tethering" your computer to your cell phone or are using a portable router or something. Otherwise, that makes no sense either. In fact, you don't even mention what version of Windows your computer is using - or if it's even Windows! Remember, you started asking about cell phones which typically use either Android or iOS. So I really don't know how to advise other than to maybe research your topics a little and then repost your question. If you need help with a concept or terminology then I'm sure people here can help with that too.
Sorry if that's being too negative. Nevertheless, I hope this clears up what hotspots are. I also hope I don't have to go into the absolute idiocy of denying updates which are absolutely necessary in order to stay safe/secure. True, you probably don't need the latest updates to something like Rand McNally's Street Finder but to not stay current with the latest virus updates is absolutely burying your head in the sand. (It's like inflating only 3 of the 4 tires on your car and then driving at a high rate of speed).