I'm starting to suspect that my 2 year old daughter, B, has a sensory processing disorder. She is over sensitive to many stimuli which leads to high anxiety in many situations. For example

Hearing: she often asks me what a sound is that I can barely hear or notice. She also gets very-paralyzingly- upset at certain noises like restroom hand dryers or electric screwdrivers.

Light: she wears lightly tinted sunglasses around half the time.

Touch: she wears a hooded jacket most of the time, and sometimes won't move until it's on, zipped, and has the hood up (sometimes with another hat underneath). She doesn't like fans, wind, or cold or rainy weather. She has severe anxiety about walking through snow. She gets upset for days after I cut her fingernails. 

Eating: she cannot bear some foods--I can't tell if it's taste or texture, but she makes a full body gagging noise if asked to eat potatoes and certain other things. If forced, she may throw up while trying to swallow. She often needs to be reminded to chew and swallow the food in her mouth (we've even made up a song to help her keep going, some meals need me to sing it for every bite)

The Internet info I've read suggests that Sensory Integration Disorder or something like it is very common with other neurological disorders like Autism spectrum disorders (which we have a strong family history of). 

So the questions I have are:
Is this something I should pursue a diagnosis for? Our insurance is unlikely to cover occupational therapy. 

Are there resources in the schools that I can access with a formal diagnosis? As far as I can tell, our district doesn't do any special Ed for preschoolers unless there's a speech delay (and B is very advanced in her speech). Is this a diagnosis that would qualify her for an IEP once she reaches kindergarten age?

What should I be doing at home? Most of her issues are things I can accommodate, but last winter she would weep and freeze if I asked her to walk from the house to the car when the wind was blowing. I need her to be able to handle things like that, even if she doesn't like it. 

Any other suggestions or issues that I haven't thought of yet?