Wow, I can relate to all you said!
I used to ride bike as a kid, but then didn't get on one for 37 years!! Now I'm 52 years old.
I guess about 10 weeks ago I started riding again, on a loaner bike, and about a month ago I got my own bike. (woo-HOOO!)
Anyway... a year ago I was very out of shape (and had accumulated 30 pounds excess weight). I started walking, and over 10 months I lost 20 pounds and got a few muscles going. Then switched to biking these last 2 months and have been pushing myself quite a bit more. I've lost another 4 pounds (only about 6 more to go!) and am gaining more strength.
I bike maybe 3-8 miles a day on weekdays, and then about twice a week I'll go maybe 12 hilly miles in addition to that.
I get out of breath going up hills, I get sore and my muscles are really straining. But I do notice that each week there IS a small difference in my abilities to get up the steeper hills. A month ago there was a ride that really whipped me- and now it doesn't seem as bad. My butt doesnt hurt anymore in my saddle. I walked up a very steep hill today that I used to ALWAYS be out of breath on...and it didn't make me out of breath much at ALL this time!

So, after 10 weeks or so, my longest ride record is 23 miles so far. I'm proud of that, and I worked hard to get to that point! I also know that if I keep at it 25 miles will seem easy one day. Remember, it's the journey, not the destination. I feel so much more healthy and strong than I did months ago, and I really love my rides- and isn't that what really counts?