Having been through the process my opinion is it's faster to wait and submit a thorough application.

You need to apply for other benefits like Medicaid and food stamps if you qualify, because it's likely you'll be denied. Starting a new application later on, might be faster than dealing with appeals, but you should be getting documentation now, regardless. Check out Voc Rehab. They'll test you and send you to their docs. If you're still healing, permanent disability might not be appropriate or necessary.

Those advising you likely make assumptions about the SSDI process.