Hi. It seems to me that your daughter presents with a lot of symptoms of Aspergers (or autism now that they have removed Aspergers from the diagnosis list). Can you send a request to your school to test her for autism? I believe they should do it for free. This way she can get accommodations in school.

Here are things you mentioned that are related to autism:
-not relating to same age peers
-sensory issues (like clothing, food, noises)
-needs sameness and routine

Does she lack verbal or non-verbal social cues like being a literal thinker (not getting jokes or metaphors), having no or lack of body language, lack of eye contact, says "weird" things that don't make sense? How are her relationships in terms of friends? Does she speak in normal back-and-forth conversations? I see a lot of the repetitive behaviour things, but not much mention of the social aspect of autism, other than lack of relating to same aged peers.

I can't diagnose your daughter or anything, and since you said you can't afford testing, I would ask your school. Some accommodations if she qualifies she could get:
-ear phones to block out noises
-schedule changes notified in advance if possible
-social stories
-services like occupational therapy for the sensory aspect

I would strongly recommend you go this route to help your daughter succeed. Hope this helps.