Please help ! Headache / migraine / backpains everything !

Yeah, folks don't get what it feels like to have migraine, ignore them if you can. Personally, I don't care what they think and do what makes me feel best.

Apologies to be rude but how old are you and if you are a female? Trying to connect the dots between your fall and headache.
When you had a fall, what it was diagnosed with? Where is your pain? Do you know your exact vertebra location of pain? (Your physical therapist will answer this question). If you still have this pain, you should continue with physical therapy. If you are not doing so, why, except for financial reasons. Did you take any meds for this, like pain meds etc. and if they helped you with migraine too.

Headahce - You seem to have migraine with auditory aspect. Do you get tinnitus? When you say, hurts at back? Where in the back exactly, between the rib cage, little below rib cage, as waist line or near buttocks? How often do you get headache? How long do they last? Have you tried any OTC products for this migraine?

Are you depressed? I agree that major family issues can be pain in the butt but are they making you depressed?

Who prescribed you physical therapy? That doc did not know why s/he is sending you to physical therapy for? I am really very sorry to hear that your mom thinks, you are faking but unless she says it explicitly, give her a benefit of doubt. The economy as it is, anyone can get fired for a petty reason and she just wants to hold on to her job.

Your fall and headache can or can not be connected. I am just not too sure but here is what you can do, Maintain a diary recording your headache episodes, record as much details as possible. Assuming you are a female from your user ID, if you have already started getting period, record that too. Talk to your mom or school nurse about it. If you are a guy, ignore this thing.
Most likely, you have a smartphone and there is an app called as Migraine Notebooks for iOS as well as Android. Its the best free app I came across. It does have shortcomings but you can still live with it. Otherwise, you can make a spreadsheet and record as many details as you can think of. More the better.

Your excel sheet can contain following columns

Date
Time Headache Began
Time Headache Ended
Any Warning Signs (e.g. Aura, stiff neck)
location of Pain (as much details as possible)
Type of Pain (Throbbing/Piercing/Pressing etc)
Intensity of Pain, 1=least, 10=Worst
Other Symptoms, Nausea/Vomiting etc.
Medication(dose) / Other treatment
Effect of Treatment (did headache end? reduced? stopped? or no effect at all)
How Headache affected daily routine (school/work/daily routine)
Hours of Sleep before headache
What I ate before headache?
Activities before headache appeared
Weather (rain, cloudy, cold, hot etc.)
Bowel Movements (Constipation etc.)
Menstrual cycle day, if applicable
Bleeding (related to Menstrual cycle, if applicable)
Important stressful events occurred today
Other medications taken today
Other comments (Anything that doesn't go anywhere else)

You could pick up few more data points from http://mymigrainejournal.com/ They do not have an app but you get a daily mail from them to record events, if any. I find that very annoying, so I prefer Migraine Notebook app (used to use spreadsheet before).

Do NOT take any medication without pediatrician's supervision. Schedule an appointment with your pediatrician at earliest and talk to him/her at length (Take all the points on a piece of paper so that you don't miss any). Eventually, you will take your diary to the pediatrician/neurologist. It will help them a LOT to figure things out.

If your mom doesn't believe you, show her this thread, may be she will believe.

If you have any questions, post it here and someone will try to help you (but you still have to go to your pediatrician).