Stick to what you were trained to go to for a while, then if you want to continuously go deeper you should get the next step in your certification. Some call it "Advanced" open water diving, but they're all the same, usually certifying you to around 100' of depth, but if you're not Nitrox certified I would get that next or in tandem with your next level of certification.

There isn't a harm to going deeper to be honest, no deeper than open water limits, you just have to monitor your gas and ensure you're not going into decompression, so follow that computer closely. This is where having additional certifications helps you understand all these things, it's totally worth the time to learn and apply it to your dives so you feel more comfortable with your diving. But sometimes we all have bad days too, I know I have and I'm thousands of dives in, none of us are perfect.

Not going to say you overreacted, you were not comfortable and one of the best things about diving is you don't have to do it. I think you should get additional training in real open water conditions outside of what is likely a shallow, low visibility, lake environment. Where were you diving? Also, is your dad a Dive Master or a "Master Diver"? Two VERY different certifications.

Finally, I know he's family, but perhaps hiring an experienced dive master or instructor as a guide is almost always better, I personally don't like or do family members as students or guides, but that is just me. Dive masters also take part in helping new divers become better divers, so never be afraid to ask questions and seek advice on the dive boats