Second opinion on frozen pipe?

Last night the supply line to my toilet froze. It's PEX pipe located on an exterior wall. The shower also has low flow, so I'm worried it's starting to freeze too. I've left it dripping slowly.

I called several plumbers, but they're all overwhelmed right now. One that I talked to told me there is really nothing he can do that I can't, so it's not worth it for me to pay him to come out. He said as long as the toilet tank is empty, it's unlikely that the pipe will burst. Does this sound correct?

Since no one can come out for several days, and it's supposed to get colder, I've turned the heat up in my house, left the sink and shower dripping, and I'm running a space heater in the bathroom when I'm home and awake. The plumber told me it's not necessary to turn off the main water supply and drain my pipes. Is there anything else I can do to prevent bursting?