Hello! Last Sunday, I was talking on the phone for around 30 minutes and after I hung up I noticed that a bug had bitten me within that time span (I am sure that no bug was latched onto my legs before that). A couple days before, a black tick landed on my arm in my house and I flung it off instead of killing it. First, the bite looked like this 30 minutes after I discovered it: http://i66.tinypic.com/2h4yo1k.jpg 
The bite was initially swollen, raised, and EXTREMELY itchy for the first couple of days. Then 3 days later, I noticed that the bite had started to take a bulls-eye shape. I have NO other symptoms of lyme disease but my friend had lyme disease so I wanted to stay safe and went to my doctor. She saw the bite and diagnosed me with lyme disease and put me on ONLY 2 weeks of doxycycline since she said I'm at the very early localized stage. I am wondering if this prescription is enough since we caught it super early or if I should ask for more? And if the chances that I will make a full recovery are high? I am a 17 year old female about to start college soon.
ALSO if the tick DID bite me, it only latched on for around 20-30 minutes so could it be possible that it transmitted lyme's disease in the short amount of time? I read that it takes more than 24 hours?
This is what the bite looks like currently: http://i65.tinypic.com/2cdjzwh.jpg It is not swollen/raised anymore but it is itchy when I touch it.