No. I think it's normal. I'm exactly the same! 7 months and googling everything. Just the other day I looked up normal movement for 31 weeks and found I believe it was on Baby Centre there were sooo many comments of other mothers feeling the exact way we do. It definitely helped calm my nerves knowing it was a common issue among us expecting mommies.
You'll be googling stuff an worrying after you deliver your baby to. We're on baby #5. We already have 4 kids under the age of 5. I'm constantly concerned about them and always googling things. I think as mothers we'll be like this till we die lol
I do the same thing and have since I found out I was pregnant. I'm 37 weeks now and I just want my boy here already lol