I am having the similar issue with my new Galaxy6. Its so annoying and making me angry why i switched iphone to galaxy. I should have buy iphone 6. My text message is getting hang. I keep pressing the button and nothing happens. So annoying.
Sorry but you are not specifically saying what is your issue other that you press "a button" and nothing happens, so you are hitting Send and it doesn't send?
It may be a lot of different things, and with SMS and MMS common issues are "almost always" carrier specific issues, not phone or even Android specific, and with iPhones users involved, it's very likely that if your messages are not getting to them is because iMessage is basically disappearing them, you should unregister your phone number from all their servers, preferably before you switch to Android, but always can be done after, and like it has been mentioned above, if you were part of group messages ask them to delete that group in order to be able to send and receive messages to those users as it should, shame on Apple for that dirty tactics that scares the hell out of the users and go back running to them after experiences such issues.
For last, the only thing you can try in your phone, IF it's a phone or App issue, is go to your Settings-Applications Manager-ALL and look for the Messages App and clear Cache and data and Force Stop it and then go back and try again to see, for a better experience and to enjoy the benefit of the Android OS where you don't need to get stuck with apps and you can switch to replace any original app in the phone, even main ones, like phone, Messages, calendars and others, you can also try Textra, one of the best Message apps in the whole store.