It's hard. I started running for the first time in my life, last summer. I'm 29 and I have lupus so I understand your pain/exhaustion issue. Running actually helps me, even when I push it. It took me a long time to work up to longer spurts. I can go 1.5 miles without stopping now... but it took me almost a year to get here!
I started out running the straight parts of the track and walking the curves. Then I ran for half a lap, and walked for 1/4 lap... then a whole lap, and so on. It's not easy, any way you cut it!! But, it does get easier!
I honestly hate running. It's boring. But, I haven't found anything else (in conjunction with my HEAVY lifting) that gets me the results I want... so I trudge on.

I think it just takes time and little baby steps! (unless of course you have medical issues)