Odd as it might sound, you could run the water heater on 120 volts. Based on the amperage you stated, it would be a common 4500 watt heater. At 120 volts instead of 240 volts (which as explain in previous answers you simply do not have), it will be effectively a 1125 watt heater (half the amps times half the volts). It will take up to 4 times as long to recover. Today's heaters are well insulated and should be able to reach a reasonable temperature even at the low wattage. You might add some extra insulation if the outside feels warm.
When I was in college, I moved into an apartment where the gas water heater was shut off and only had a lit pilot. I merely noticed it was taking a very long time to recover (nearly all day). But it was enough to shower once a day. I did this for 3 months before finding out that it was never running the main burner. Running the electrical elements on half voltage should be better than a pilot.
I'm also concerned about adding extra load to the remaining side of your panel. That could easily cause the crippled main breaker to completely fail. We don't know why it failed on one side. Why would that trouble not also exist on the other? This is something that needs fixed sooner, not later. These larger breakers are often similarly sized and a new one from another manufacturer may fit (have an electrician do that work). The connections in your photo are what is common in separate large breakers.