From what you have described, it’s very possible you were overweighted, which can be dangerous. It also sounds like whatever was going on with your neck seal may have been dangerous (a strap??). Also, were you using a steel or aluminum tank? As a woman who dives mostly with other women, I have seen that women trim out better in a steel tank because it distributes some weight further down by your hips where most women have their center of gravity/buoyancy. It’s likely your trim was not optimized, which can make buoyancy really hard to manage. A lot of times, male instructors are not aware of the best ways to configure trim for a female diver. You can do some research on online female diver forums to understand the best way to configure your trim for your body type prior to your next class.
Don’t be discouraged by this negative experience, but please look for a reputable instructor—by name, with references from people you trust. Also, if you eventually plan to dive very cold water, I’d recommend getting certified (or getting practice after warm water certification) in moderately cold water such that you are wearing a 7mm wetsuit and thick gloves and hood (e.g. UK, west coast of US/Canada, European lakes). This will give you practice with the more cumbersome gear before you start using a drysuit. Good luck!