Jury Summons. Can I claim the "primary caretaker of a person who is an invalid unable to care of himself or herself" exemption?

I'm the caretaker for my elderly father and mentally handicapped sister. My dad took a bad fall last year and still recovering from it. He's able to get around on his own in the house but requires use of a walker if he goes outside. He has trouble balancing when walking and gets confused easily. If anything happens to my dad my sister goes into panic overdrive...screaming, yelling, and generally freaking out (she's loud enough to wake the dead). She's 42 but when in panic mode she's mentally about 5 or 6 years old. In that state, she won't think to call 911. Which means if something happens to dad he won't get any help unless I'm around to make the call. Neither of them are truly invalids since they can get along without me for 3-4 hours as long as nothing happens. Any longer than that dad gets extremely upset thinking that something bad happened to me. ...and my sister also starts getting panicky. My dad has heart problems and is diabetic so my sister's panicking certainly isn't helping.

I'm physically disabled myself and can't walk the 2 blocks between jury parking and the jury building. I don't have a wheelchair capable of accommodating my size. I can't claim a health exemption since I'm not on disability and can't get a doctor's note without paying $250 for an office visit. My dad thinks I should take the "primary caretaker" exemption but I'm worried about getting fined for taking a false exemption.

I'm in Harris County, TX if that matters.