If I had to classify it, Young Adult fiction would be the genre, but it may just be broader fiction with a mostly teenage main cast.
I don’t remember much about the main character but he has some sort of power that I believe awakens, and he ends up on the run. He eventually comes across a mysterious girl and her relative (grandfather, I think) who rescues him and comes along with him. This girl seems to be able to see the future, and knows about him and that they will eventually be married. I also believe that she can talk to animals, though this may not be the case. Her grandfather has trained her to fight and specifically talks about fortifying the house they were staying at with steel embedded in the door, before the government( or some evil corporation potentially) comes to get them.
I believe neat the end they find yet another youth who has powers, and end up infiltrating some sort of cult compound.
I’m pretty sure that it’s a relatively recent book, maybe 5 years old at most, because the sequel hadn’t been released yet, or it may have been a one off, I’m not sure.
The Outlaws Scarlett and Browne by Jonathan Stroud has many of those plot devices.
This made me think of “A Spell for Chameleon” by Piers Anthony — only it’s written too long ago. You might give it a try it anyway.