No, I would not say you're insecure.
Insecurity to me means one doesn't (believe in them self). They lack self-confidence and worry about how others might view them.
Trust is much like respect in that it should be (earned) over time. Before one trusts someone they should allow them to demonstrate their "trustworthiness" over a period of time.
Some people have adopted the: "I'll trust anyone until they prove me wrong." philosophy. That's a conman's dream!
Being gullible isn't a virtue!
In some relationship situations people have been known to attempt to "shame their mates into trusting them" by accusing them of being "insecure" or "paranoid". They may even say you have "trust issues".
Their primary goal is to get you to stop asking them questions! People hate being described as "insecure" so they stop asking questions.
Asking questions doesn't mean one has "trust issues". However not getting "honest answers" to their questions can cause trust issues!
Open honest communication is what solidifies relationships. Anyone who is in a relationship where they feel they can't say what is on their mind or ask their mate questions when they arise is not being true to them self. You'll never truly be happy unless you can be you!
Never separate your mind from your heart when making relationship decisions. The purpose of the mind is to protect the heart.
If something doesn't feel right to you then it's probably not right for you. Know yourself, Love yourself, Trust yourself.
If you have to "change" who you are to make a relationship work it means you're with the "wrong person". The goal is to find someone who will love and appreciate you for who you are!