TinySine 3G Shield Troubles

Hello all,
I am using an arduino uno and a tinysine 3g shield with the sim5320A chip inside. On their website, (3G/GPRS/GSM Shield for Arduino with GPS - American version SIM5320A), it says to use the ADAFRUIT_FONA library with it, so that is what I am doing. When I try to send a text from the FONATest sketch, it allows me to type out a text and it says Sent! so I suppose the arduino thinks it is functioning properly, but my phone has yet to actually receive a text, so clearly something is not working properly.
This is what it prints out(number changed):
s
Send to #15555555555
Type out one-line message (140 char): hi
---> AT+CMGF=1
<--- OK
---> AT+CMGS="15555555555"
<--- >

hi
^Z
Sent!
FONA>

Any help would be super appreciated!

The debug listing appears correct, but if you can, please post your sketch within tags.
I've used many of this modem shield - and it does what it says on the box, but I have heavily modified the original FONA library to my own purposes (including multi-part text messages!)

BTW: I have found that all my SIM 5320 shields arrive preset for 4800 bps serial.

Assumption: Your phone number is 15555555555 (or whatever)
Unlikely, but your telco may want the international +NN prefix on the number. Usually on;y necessary if you are crossing borders.

Next step is to eliminate FONATest, and use a direct terminal session to the modem - so you can see each message & response.