Betta sitting on top after water change

Hello! We have had our fish for about a month now, and my mom changes the water once a week. She doesn't perform a complete water change, but she does change most of it. Ever since she's changed the water a couple of hours ago, our fish has not been moving at all. We gave the bowl a couple of taps to see if he's alive (we know we shouldn't have, sorry), and he did make sudden movements. I also read that the water might have been too cold, so we added some warm water. He swam for a few seconds and completely stopped again. I have attached a picture. Could you please help me out? I feel like I'm gonna cry.

from all the research i've done, i've heard time and again that bettas (or any fish, really) should never be kept in bowls. the ammonia levels rise quickly from the fish's food and waste, and because the bowls are typically very small, this can lead to lots of issues, including diseases and parasites. a weekly water change probably isn't enough if you're going to keep a fish in a bowl. aside from the ammonia issues, you have other issues as well. the cold water is one of them. bettas are tropical fish and if the room you keep the betta in isn't always around 75-80 degrees Fahrenheit, you probably need a heater. despite what you may have heard a betta will also do much better with a gentle flow filter which i'd imagine you also couldn't install in a bowl. i'd recommend buying a tank that is at least 5 gallons for the little guy, and in the meantime you or your mom should do some extra research to ensure the betta's not sick, has the right diet, etc.
i'm no expert. this is all based on what i've read on forums and websites dedicated to information on bettas.

OK, as has been noted above your main issue is that your fish is in a bowl without a heater or a filter. This means the water temp isn't constant and you probably have ammonia and nitrite in the water.

So you need to do more than one water change a week. Also you need to add some interest to the tank for your betta. What he's living in right now is the equivalent of a bare 6x6 cell for you. There is nothing to stimulate him in any way.

As has already been suggested you probably need to buy a tank that you can put a heater and filter in and some live plants to give him something to look at.

Sorry to sound so negative, but your fish is not happy right now and you need to do something to sort the situation out ASAP.

That bowl while small could work with a heater in it, you will also need a lid Bettas are notorious jumpers.

Heres what you could do with the bowl. Image NOT my work.

Your fish needs stimulation, fun fact: fish like living in enviroments with lots of stimulating factors, plants, invertabrates, other fish. As previously stated a bowl like that is a no go. Please do some research before buying an animal, and please do take our advice, we all want whats best for your fish