To add to what golja says:
The root level domain is never handled by a subdomain or subdomain wildcard. Essentially anything that appears before the period of the root domain indicates a subdomain from the root, it does not modify the root.
So, regardless of any subdomain wildcards or even subdomain records you create, the root domain will always have to have an
A record or
CNAME (although not highly recommended).
Your DNS config should look something like this:
A | mycompany.com -> 22.214.171.124
A | *.mycompany.com -> 126.96.36.199
This should give you the following usable DNS records:
- etc. etc.