iMessage not working on brand new iPhone

My iMessages are not working on my brand new iPhone, but they also wasn't working on my 6s. Brought it to tech support ant the only thing they could see that was wrong was that my phone was so old and battery degraded that it must be the cause. Thought getting a new phone would solve it, but something seems to be wrong with my iCloud account since I have troubleshooted every other possible way. Anyone else have experience with this? I have tried everything from restarting iMessage to restarting phone to signing in and out. Even more frustrating is I can sometimes send text messages, but I receive iMessages back from those I send texts to. Also can send and receive some iMessages on my laptop, but obviously they are coming from my email.