Yep I agree with doing negatives. I couldn't do any when I started and that's how I developed the strength to do so. I can't do a huge amount, around 10.. but it's a massive improvement from where I started.

What you're doing isn't likely to make you stronger, the muscles work differently in different parts of the motion - and yours are not seeing any load beyond that bottom few inches, so they won't adapt and grow stronger in the upper part of the movement.

A better way to work up to pull ups is to do the negative portion of the motion until your strength improves. Either jumping or using a stool, raise yourself up so your chin is above the bar. Lower yourself slowly in a controlled manner back to hanging, then repeat. While you can't lift yourself up currently, your muscles are stronger through the negative, or eccentric, part of a movement. As you do more and more of this, you will get stronger, you'll get better at working the muscles together as a unit, and progress to full pull ups.

Sore is becouse you are starting to use muscles that you are not used to using, it is normal and every single time you start a new exercise/activity, you will be sore for a couple of weeks and then it goes away. If you stop, you'll have to start all over again and have to go through being sore all over again.