Is there a way to send a (sms) text to myself when I receive a new Gmail message and the subject contains a certain string?
Is there a feature in Gmail itself, a third party service, or an addon that would help me do this?
IFTTT (If This Then That) may be able to help you out. You can find Connect Gmail to SMS recipies here.
I don't know of a way to get it to send an SMS, but there is a solution if you have an Android phone.
I have my Gmail set with a filter (in settings-filters) to set a label ("notifyinandroid") for certain senders, then I have the Gmail app on my phone set to only notify me when items arrive with that label. You could also do this for certain subjects.
That way my phone will notify me if I have an email from somebody that I care about. This setup works great for me.