You Deserve to Brag!!!
You're doing awesome and you're going about it exactly right! Just keep going! Slowly -- very slowly -- jog more and walk less. Especially because you mentioned your joints hurt, it is important to take it slow. Your body needs time to adapt or you will injure yourself, which will set you back (I learned this the hard way).
When I first started I mostly walked, I could only jog for a minute or two at a time, and I didn't like it much either. It was just so painful and hard! Everything hurt. A whole mile would've been out of the question. But slowly I started being able to jog for longer, and needed less time walking between bursts of jogging. At some point I started being able to jog a half mile. Then 3/4 mile. Then a whole mile, and... you get the picture!
Now I run 6-8 miles a day, 5-6 days a week, and I actually enjoy it. If I don't run my legs start to feel like they are just itching to stretch out. I can even do long runs of 10-14 miles if I have the time.
Just... keep... going!