Set off alarm when receiving text from a certain number?
Kinda. If you go to your sound settings and change the default text tone to "none" and then go to your contacts and change the text tone for whichever contact you want a notification from to something that DOES have sound, you will only get audible text alerts from that specific contact. 

However this will not work if the phone is muted, or if Do-Not-Disturb is enabled.

I just tested this theory and it works.  Hope that helps!  ;-)