Check out third-party texting apps so that you can text your boyfriend without anything showing on your phone bill. Make sure you both download the same app.
Texting apps especially for iPhones include textPlus (free), TextFree Unlimited (free), TextNow (free), Textie Messaging (free), and TigerText (free).
If you have another kind of smartphone check out Whatsapp (free for 1 year and then $0.99 each year thereafter), Kik (free), WeChat (free), imo (free), KaKao Talk (free), Pinger (free), and textPlus (free).
Of interest, Kik recently announced that it now has more than 50 million users and that iOS and Android versions of its app just became available. People are signing up at a rate of 200,000 a day. Kik users send two billion messages every week.