What you could do is find a friend or neighbor who has a shelter or basement with a reinforced area. Then you could go hang out there while the storm rages and if you need to seek underground shelter you'd already be there.
This is what I tell my family. If you know a storm is coming and it has rotation in it or you have the possibility of a tornado it's better to see it coming and take precautions before the storm hits.
Go to that friends house and play games, cook snacks, watch TV and listen to a weather radio.
You have to find a safe place to go that is not your house evidently.
I say this because I grew up a couple of miles from Moore Oklahoma. I know what it's like to hear the sirens and go to the storm shelter. My mom and dad built one in the back yard and it was big, like 10X10 or 12X12.
We'd go sit on the covered patio and listen to the radio while playing games. It was the best time ever. When the sirens went off we'd scoot into the shelter.
Just a point that I have to make.
Last month Moore had another tornado. Actually the channel 4 helicopter got video of 3 on the ground at the same time. There was an extremely low chance of tornadoes with that storm but yet they still had several at the same time. If they'd have met up and gained strength they might have formed a much more destructive situation.
I go to my shelter place in plenty of time so that I'm not caught out in the storm. It's better to get there before the storm even hits your county. Why wait? It's coming and it has a potential risk for injury.