Traveling with peps

I’m headed down to Florida for a few days this week & I’ve never travelled with my peps before. I got an insulin case thingy with an ice pack from Amazon, but I’m wondering if I should bring the vials & empty syringes to fill as needed once I’m there or should I pre-fill & travel with the syringes only? Somehow I feel like pre-filling would make them leak or I’d lose product or something. If I’m calculating correctly, I’d be bringing about 16 syringes with me if I prefill. What do you think? And will TSA care either way?

Thanks!!