speedy
I use Skype all the time when travelling (and sometimes at home) to send text messages and for phone calls. After you press the send button, the history line above the text box should say "sent" and a few seconds later "delivered".
I've only experienced one hotel a few years ago hampering Skype and only on very rare occasions is the message "pending" for any length of time. If you are getting this frequently from one location then it may be being throttled or blocked in which case call the ISP to check.