You could simply drop the Arduino idea, and use an ESP32 - much faster, more powerful, and has WiFi built-in - basically an ESP8266 on steroids
Once you've got an internet connection, then I would suggest ignoring all the hassles of static IP addresses, port forwarding etc. and do what I'm currently working on at work (following on from my home system).
Use the ESP32 (or whatever) to read your sensors, and then send the data to a server somewhere - as long as you have a website of your own (that has PHP and MYSQL) it's simple to do, or you could use an existing service, such as ThingSpeak as my home system currently does - I've never got round to altering it to my server yet, as it's mainly for experimental reasons.
This is my home system, uploading via WiFi to ThingSpeak:
And this is my current experimental system at work uploading via GPRS (the project is about developing and building commercial GPRS systems), I added the temperature and humidity sensor to give some live data, and it's on test waiting for the batteries to go flat (it's been running just over a week so far, from 4 x 18650 LiIon batteries in parallel - there's a protection board with the batteries, so I'm expecting that to shut the batteries off before the project itself stops running). For the purposes of this test, it's transmitting the readings every five minutes (so 288 readings a day), and while the GSM modem is turned off between readings, I've made no efforts (so far) to reduce the processor current - which is an 18F PIC running at 64MHz.
Assuming it's cheap to use GPRS in the USA? (as it is here), then it might be a far better solution than paying for Internet, or paying to borrow your brothers?. SMS is pretty expensive here (around 5 to 15 pence per txt message), where my 288 uploads per day are only costing about 1 pence per day on a pay as you go SIM card. Assuming a txt is 10 pence, that would be £28.80 per day!!.
One
BIG advantage of uploading to your own server is that you can do a great deal of the programming on the server itself, all the remote unit has to do is upload the data to a MYSQL database (it does this via a simple PHP script), and everything else can be done in HTML and PHP on the server, accessible from anywhere in the world. You could also easily set the PHP script (that uploads the readings) to send you an email when it does.
If you look at the battery voltage graph above, you'll notice that it's scaled from 3V to 5V - this was based on my assumption that the protection board will cut-off around 3V - assuming it doesn't, I'll simply edit the PHP script that draws the graph (changing a single value) to lower the bottom limit (probably down to 2.5V or 2V - as it shouldn't go below 2.7V).
I've also got a wager coming up - many of the envisioned uses for the project will use non-rechargeable LiIon, as existing GSM types do - and these commonly transmit once a week only, with an expected five year battery life. The batteries are 19Ah, and usually used with at least two in parallel, with a 'best' capacitor across them - the batteries have high internal resistance, so can't supply the high current pulses the modems require. So the next test will be to power it from one of these batteries (adding a best cap - I've got a space for it on the PCB) and see how long that lasts. My boss reckons that it will last more than 60 days, I reckon it won't make 60 days - so we've got a bet on it, with the loser buying lunch!
As the 18650's haven't run out yet, it's a bit difficult to predict - the 18650's are 2.2Ah each (so 8.8Ah), but are second hand batteries - so that makes it even more difficult. I'm guessing they won't make three weeks - if that proves the case, and they are truly 8.8Ah, then the 19Ah shouldn't make 60 days!.
Anyway, enough rambling on, hope this gives you some ideas.