There are a number of cost-effective DIY ways to improve the security of garage doors from the inside.
If it is for a prolonged period, one can prevent the overhead door from being opened at all, by unplugging the garage door opener and using a padlock along the side rail.
In addition to the Garage Shield mentioned earlier, one can zip-tie the emergency overhead door release. If you need to use it during a power outage, you can just clip it and replace it.
For a few dollars, you can install a garage door inside deadbolt lock.