I’m trying to avoid using a lawyer for my claim. But of course, the USAA agent is lowballing me because I don’t have a lawyer.


Your comment isn't very specific.  I assume you are talking about a total loss auto?  You could also be talking about a settlement for a bodily injury claim which is more of a judgment call. 


For auto, you need to find several like automobiles (same condition and miles) in your area to use as documented proof of value.  A car in California may be worth more than a car in Louisiana due to income levels in that area.  A Blue Book price is respresentative of the country or region as a whole and may be over stating your area.  A common practice of insurance companies is to say a vehicle is for sale at that price but probably sold for less.  If you can find at least 3 other vehicles that are identical (at least within 5,000 miles or so) and verify the sold price, you could use that in small claims court and avoid a lawyer.