Does my new phobia/fear have a name?

My top phobia/fear used to be medium-large dog breeds. It's still my fear and I have respect for powerful breeds (pitbulls, Rottweilers, Cane Corsos, etc) and avoid getting close to them; maintain a distance. I guess I have healthy, reasonable fear because they can injure or kill us.

Now, a new fear overrode that. Ever since my son was born nearly 3 months ago, I've become a safety freak. For instance when going up and downstairs at my grandma's, I held my baby in a carrier; walking much slower than usual. I got slightly criticized for going too slow. I didn't care. I'd rather be slow but keep my baby safe than fast and possibly trip.

My fear is my son getting hurt, anything happening to him. I've seen videos of babies climbing out of cribs as well as read horrible stories of toddlers running around in the kitchen (I'll have a gate install when he starts walking so he doesn't go to the kitchen) and accidentally knocking into a boiling pot, getting burned, rolling out of beds or falling out of windows, etc. Now it's like I've become overprotective with my son, esp over things that can harm him. When taking him out of the car seat, I do it carefully, gentle and slower but at least he hasn't bumped into anything so far.

Seriously is there a name for that?

Updates
10 mo
This doesn't mean I won't let him learn things. I've been estimulating him every day with new activities. I'll take him to swimming classes when he turns 5-6 months. I'm just very cautious about things that can hurt him. I don't want him ever getting hurt badly.
Does my new phobia/fear have a name?
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