Help!: New Runner Swollen Legs

My thighs and hips are my problems areas. My husband who was in the military told me that if I started running, that would really burn the fat off. So, in the past two weeks I have started running. Saturday I went to workout and sunday I noticed that my pants were really tight in the thigs. (annoyingly tight). They have been this way since I started running, just not that bad. Is it normal for your legs (thighs) to be swollen like that? I ran 1.5 miles in 20 minutes on that saturday. I have never ran that far in my life. I quit smoking 5 years ago and never ran prior to that either. I got on here so maybe some of you veterean runners can guide me in the right way or offer some words of encouragement. I really love running and now that I have started, that is my preferred way of working out. 

I also need some good advice on what is a good running shoe.

Thank soooo much!!!!