Hello and sorry you're having problems. It is very possible that the touch LCD panel has failed and requires replacement. However it would be worth trying a hard reset of the Kindle to see if this helps:
To do this, simply press and hold the power button on the Kindle for 30 full seconds, then release and wait a full minute for it to reboot.
Do not press anything else during that minute. If this does not cure the issue, oftentimes the reset procedure needs to be repeated several times for it to force a reboot.
If you're still running into problems, then try plugging the Kindle into the charger for 15 minutes, then eject it and try the reboot a couple of more times.
This clears up the issues you're having 90% of the times, but in the rare case that it does not, the problem may go deeper than a software issue.
In this case the entire LCD display of the Kindle would need to be replaced.
If this is something you're looking to do yourself, then please check the back of the Kindle to let me know which Kindle Fire you have (HDX6, HDX8, etc.) and I can search for a link to parts.
Alternatively there is a 3rd party Kindle repair service that can fix this type of problem and you can contact them at the link below if you'd like:
Feel free to reply back if you need more help, or want to reply back with more details. It does not cost you anything more to reply back once you've rated. Please do rate me positively (at least 3 STARS) and I will continue with you until this is sorted. The positive rating ensures I am credited for my work.