The whole leveling experience of a new player... is this?

[SturmChurro]

I do the story quest chain and I always end up under leveled and hitting the level wall for the next story quest. Mind you I am also doing some or most of the side quests.
It's gotten so bad, that I am currently level 32 and after starting the next main story quest after the lvl32 wall, I ended up being at 30% of my exp bar and not being able to continue with the story quest. This constant abruption is really turning my experience into hell. Most people are telling me that this should not happen.
In the end is this thing normal? Or am I not doing something right?
Thank you in advance.

I was always overlevel, but that could because I would always stop and do fates, do all the sidequests, and I would also queue up dungeons everytime I got a new one just to get the first time bonus exp (and I like doing dungeons). I never had an issue keeping up in level even on HW content. You could say it's really grindy, but it worked.