I handle FMLA and Short Term Disability as my job so below are a few notes. Feel free to PM me with any questions. I can't answer whether or not you are eligible, but I can tell you the eligibility rules. In order to be eligible for it, the following must be fulfilled.
1) You have to have been employed longer then 12 months at same company
2) Worked more then 1,250 hours in past year
3) Your employer has to have more then 50 employee's in a 75 mile radius
That's the basic eligibility rules that everybody is required by law to follow.
There is two types of FMLA as well, continious and intermittant. Continious is for a set period of time, IE for 3 weeks solid from 11-07-2011 to 11-30-2011 or something like that, but you can also get it intermittant ( which in your case, is prob what you want or need ) where you can get it set up as episodic, which for example, when my dad was in hospital for cancer, I had it set up under approved ILP for 3 absences a week, each one lasting up to 1 day.
Whatever time frame you get on an ILP or continious, is entirely dependant on the doctor who fills out the paperwork. Most doctors are very familiar with the process and be willing to work with you, just let them know what you are requesting. Some doctor office's charge a small fee to fill out FMLA paperwork, some do not.
PM me any questions but trust that clarifies a bit for you.