I am in Kenya and the twilio pricing is very expensive here. I would like to send and receive sms messages, store them in a database and display them on a web app. Is it feasible to build this with node.js? How could I get a framework like express to send/receive text messages?
I did some searching and found a similar service called SMSified, that seems to be priced more reasonably. There is a node module that hasn't been updated in 3 years, but that might give you a good starting point.
Another one that is explicitly free during development/testing is Tropo. This one has a more-recently-updated node module.
I haven't used either of these myself, but hopefully one of them should be what you're looking for.
Another option is to use an SMS gateway provided by the carriers. Typically you can send an email to [number]@[gateway-address]. For example, to send a text to 123-456-7890 on AT&T's network, you would simply send an email to 1234567890@txt.att.net. Take a look here for a list of common carrier's gateway addresses.
If you already have email integrated with your app, this might be very easy to implement. The only downside is that it would require users to specify their carrier before you can send them an SMS message.