^ $130 is I guess because they are counting the weight in pounds, so every additional pound is getting charged a lot. I'm guessing the guitar in it's case is weighing in at around 10-14lbs?
Carry along luggage doesn't get charged, but I believe some flights do not allow certain luggage of particular dimension to be carried along with you on the flight.
Anyways if you are being forced to place it in the cargo hold then a flight case is needed. I'm not sure what kind of case that guitar comes with, if it's hardshell then make sure that it's extremely durable. depending upon whether it's a direct flight or connected flight the amount of abuse it will receive is going to vary during loading/unloading. Since you already are in US then getting hold of a really high quality flight case for cheap shouldn't be a problem, they usually have a lot of stuff getting sold for used all the time there on Craiglist/Ebay. Goodluck with the trip.
PRS SE[Soapbar,Semi Hollow], Fender Squier CV Strat, ESP LTD Viper 400, Laney[LH20 head, LC50Mk.II, LX65R], GS412IS(WGS ET65 loaded), Boss TU3, Dunlop ZW45 Wah, Boss GT10, Shure SM57, Sennheiser E614, L6 Pod Studio UX2, Abelton Live 8, Reaper, Seymour Duncan[SP90-1,SP90-2,SH10 bridge,SH4,SH PG1,SH55], DiMarzio[DP100,DP159,DP103]