As mentioned, the tire diameter marking as 28" is somewhat ambiguous and can refer to an actual bead diameter of either 622mm ("700c" size) or 635mm. You probably have the 622mm size but it would be good to check the tire carefully to see if either 622 or 635 are printed on it anywhere. If you have the 622mm size then Tannus makes their solid foam type of tire in both 32mm and 40mm widths and either of those should work with your wheels. But note the comments that I and others have already made about disadvantages of using non-pneumatic tires.

You keep saying that you need to fill them "every single time" you ride, but give no indication of how often that is. As mentioned, it's normal for air to slowly diffuse out of bicycle tubes. So if you only ride once a month it wouldn't be unusual to have to pump them up every time. OTOH, it would be unusual to have to do this if you're commuting by bike and therefore ride at least twice a day. As fietsbob and I have already said, switching to the thicker 'thorn-resistant' tubes would give you a thicker rubber wall so the air would diffuse more slowly and would only need to be pumped up every couple months instead of weeks. These also have drawbacks of greater weight and increased rolling resistance, but not to the same extent as solid foam tires. (And tubes stretch so the ones made for 622mm rims would also work ok with 635mm rims.)

I'm puzzled by your comment that "I haven't found anything online in the city I live" since a big advantage of finding things online is that they can be shipped from almost anywhere in the world.