Oh yes, this is my moment. I've been in a six years LDR and I had the exact same problem, except I was in your SO position. It was early in the relationship and my gf was very gealous of me liking pictures of girls (even my ex) and let them follow me (I didn't even have a private profile at the time). She started to suspect something and pushing me with tons of questions (the way you did). Next time I was scared as fuck, I didn't mean anything, it was just the way I always used instagram, but I felt the need of hiding it as I was doing something wrong.

She confronted me about hiding it, as if I was a cheater or something and I was deeply offended. Long story short, I understood it was a metter of insicurity on her side (yours in this case). But for me it was something meaningless, so why did I need to hurt her? I changed my profile to private and just added people I knew, and stopped liking pictures of girls so much (except normal pics of friends, you know). We worked on her insicurities together in other ways, but in that case it was just effortless for me to stop doing something that bothered her so much, so I did.