Hi Vicky, I have the same problem with my pinky on the bass E string, especially closer to the body of the guitar. What I've found when running through spider exercises along the entire neck is that I need to adjust my hand, arm and wrist positions while working horizontally. My wrist and fingers are pretty damaged and arthritic from doing deep tissue massage for a couple of decades, and I sometimes get a hint of carpal tunnel nerve pain if I do too many exercises. Just take it slow and be patient with yourself. I've read that it takes 100 repetitions of a movement to get that muscle memory established and there are shortcuts to getting there. Focus on your precision with every repetition most importantly. These can be done in quick succession as such, place your finger as stated above like you're drilling that fingertip through the fretboard, right next to the fret, pick it up off of the string and do this over and over again. This can be done while watching TV or listening to music. Think of it as something to keep your hands busy instead of smoking a ciggie. Ha.
The pinky is a problem for everybody starting out. The one thing that I've found has some incredibly useful exercises to address pinkie agility and strength is this 30 minute daily warmup video. I would not recommend doing the whole video initially, but maybe select some of those exercises targetting your weaknesses and built up from there. I started out trying to do this whole video everyday and soon came to regret it. It's amazing, but at an advanced age with much mileage on the fingers and wrists, plus being female to top it off (we just don't have as much room in our wrists for scar tissue as men), it's best to break it up in bits throughout the day or week.
I hope you find this as useful as I have. Some of the best exercises here for the pinkie finger are the hammer ons, pull offs and legato runs. Frustrating at first, but if practiced diligently, will have that finger following orders just like all of the others. As for the wrist, it helps doing some wrist rolls that pinpoint the sticky spots you can gently stretch to make them more limber and mobile.
Oh, and welcome to the flaking fingertip club! It sounds like we're in very similar places with learning. Maybe we can share resources to keep that motivation going.
The internet is loaded with helpful resources we could only have dreamed of as youngsters. I'd have bankrupted my parents by now with all of the free stuff I've found online.