Worried about step daughter

Anna
My step daughter is 5 years old and while she is very active and can be social, I'm starting to worry about her behavioral issues. 
Let me start with her sensory problems. Putting on socks is a huge issue because she will throw a tantrum if she can feel the seam of the sock. Also, she hates flushing the toilet because the loud noise scares her. And brushing and washing her hair has always been a struggle. It doesn't matter how soft you touch her she will cry and say it hurts. Now, some of this is normal once and while but this is daily. 
If she can't do something right away she throws a tantrum. We've been attempting to reach her how to tie her shoes and she gets so easily frustrated. 
I realize that tantrums are normal once and while. But she loses control of her emotions daily. 
We started getting to see her regularly again, 4 months ago, after more than a year of just 4 hours a week because of her mom. So we're having a hard time figuring out if this is just really bad behavior or something deeper. I just want to know if we should be handling her behavior from a different perspective.