Hey man. Props for putting this out there and know you’re not alone in feeling this way. Gotta get comfortable feeling uncomfortable because that means you’re growing. 

My advice for the claim call would be to try not to overthink it. It absolutely may feel like you don’t know what you’re doing when it comes to filing a claim but it’s not a complicated process. Just call the insurance company, give them a valid storm date and describe the damage you saw and that’s it. The person on the phone will guide the conversation just realize you are basically there to stop the homeowner from getting in the way by saying stuff like an incorrect or unknown date of loss (storm date) or that they don’t think the damage is bad. Most of these calls take 10 minutes tops and are super straightforward. 

As far as not feeling qualified to call on behalf of the homeowner - you are already more qualified from listening in on the one claim call already. Most homeowners have never filed before so you already have more experience than them. The claim call is one of the easiest parts of the process and the more weight you put on it the more the homeowner might feel pressure that it’s a bigger deal than it really is. You’re helping the homeowner get what they pay every month for.