Chances may be good to get SSI for son. As for you they are probably just following the rules that say to get state assistance you must be denied ssi. Alway a lot of hoops to jump thru
Good luck

Also getting SSD or SSI is based on the ability to work at any job. Its a bear to get thru the system. It took two years before I was able to get SSD. They are very strict about receiving SSD, or SSI. You must be disabled and unable to hold ANY job. The more documentation you have the better. Usually people are denied the first time around but you should never drop the application. You need to preserve the application date. Always appeal a decison. Then if you win it will go back to the original date of application and you will receive back benefits based on that application date. That is why it is very important to preserve that date. I used to do disability determinations for the state of Florida. Also I got SSD myself years later and it took two years and one appeal to get it. It can be extremely frustrating!!!!