99.9999% of people have some sensory issues. It is a perfectly natural thing to have. On the other hand, for some people those natural things are so severe they interfere with their life. it is at that point that therapy is needed.
Since she is rubbing herself with pudding and eats playdoh, you can assume she does not have a tactile sensory issue or an oral sensory issue. She could crave sensory input (which is fairly normal for many toddlers) or she could just be exploring her world.
As for the autism thing, remember that for an autism diagnosis she has to have a SEVERE social interaction problem, which is NOT cuased by her speech delay. At such a young age its difficult to tell the difference between the autistic social delays and social delays caused by speech delays.
For example, some of the things they mention in Alex
1) he tends to avoid eye contact
2) He does not seem to engage other people in most social interactions (but if he is one on one or two on one he will)
3) He has little to no conversation speech (He cannot sustain a conversation, but its unclear whether this is being caused by his expressive speech delay or by something else)
4) he is very routine, but he is also starting to adapt where things can be changed on him with explination
5) Echolalia, he repeats things a lot, this is also a normal thing for kids to do as its part of the learning process of langauge. He will repeat things when h is bored, but he will also use canned phrases when he doesn't know the right words to express himself, over the last year this has started to diminish quite a bit.
6) He is extremely active, he also takes his shoes off whenever he can, and we have spent the last year working on getting him to not scream bloody murder when washing his hair or getting a hair cut.. its improving, slowly but it is.
Alex was also on a bottle until almost age 3, it was a routine and we were not able to break it until Mason came along (and suddenly bottles were for babies not big boys). Both my children love to be naked, they strip whenever they can. it is a normal phase for those between 18 months and 4 years old. Alex does it less and less now at 4 and Mason more and more as he reaches 2.
It sounds like there is some mixture of pickiness on food and I am not sure how they fix that, but for it does sound like she is seeking out sensory (rubbing stuff on hrself) and the way they work on that is by brushing (a simpler way of doing this is to take something soft and using some pressure rub it up and down her arms, back etc..) and weighted vests, though also remember its not THAT unusual for a 3 year old to cover themselves in messy stuff like paint, pudding, etc.. (Alex used to rub his applesause into his hair) Here, the closer he got to 3 1/2-4 the more these things disappeared.
One book you might want to read is the Out of Sync Child, which deals with sensory issues in Children. Also one of the keys is to recognize what sets your child off and try to limit/avoid those situations.. like I know that I can take Alex out for 1-2 hours before he will need some quieter time to refocus himself or he will start to get whinny and tantrum because he's over stimulated.
Alex was evaluated for sensory issues and his OT said he had some moderate issues (she also gave us tips to work on the hair thing) but they were not severe enough to require treatment, but she did work on his ability to retask himself. Over the summer he went from not being able to move from one task to another within 60 minutes (without tantruming) or moving from soemthing he loved to something he hated without tantruming, to being able to change tasks every few minutes with little to know tantuming and it didn't matter how much he liked hated the activity.
It may be worth while to see if your insurance will cover a consultation wtih an OT, even if they won't cover the therapy, the OT may be able to give tips on what you can do on your own. Another option may be contacting an OT program near you to see if they do free evaluations asnd therapy or reduced cost stuff for student training. Some insurances will cover evaluations but not the therapy after that.
It is very hard here to get OT therapy for sensory issues since the state and school district do not recognize it as a seperate OTdisorder, instead you have to have another OT type delay (gross/fine motor skills) in which they then treat the sensory issue as a secondary thing that plays into the other delay. If its all sensory usually you have to do it privately.
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Mommy to Alex (4)and Mason (1 1/2)
Law Student - 1 year done, 2 to go