Welcome to our Forum. I'll be pleased to comment. In terms of HIV this was a no risk event. Even if your partner had HIV (even among commercial sex workers, the majority do not have HIV), there has never been a case of HIV documented to have been acquired by receipt of oral sex, not even one. This is the case irrespective of mouth sores, bleeding gums, dental disease in the person performing oral sex. You will not be the first. There is no medical reason to even test for HIV related to this exposure.
Several STIs are occasionally acquired from receipt of oral sex. Nongonococcal urethritis (NGU) due most often to acquisition of mouth bacteria into the urethra is most common and more rarely Gonorrhea can be acquired from oral sex performed by a person with gonococcal pharyngitis. Both of these problems are typically symptomatic, presenting with burning on uriantion or a penile discharge. If these do not occur in the few days after sex, you realistically have nothing to worry about.
With this as background, on to your specific questions:
1. Is there any risk of HIV for receiving blow job ? Knowing that I didn't notice any bleeding from CSW mouth .
Please see above
2. The time of the rash is after 4 weeks of the last exposure . Is it related or late. ?
Four weeks after exposure would be quite late for the ARS to occur - two weeks would be much more typical. When it does, the rash, if present, is typically accompanied by high fevers, severe sore throat and muscle joint aches. Your symptoms do not suggest the ARS to me.
3. I didn't have flu like Symptoms no fever no night sweats is this a good sign ?
This is also evidence that this is not the ARS- see above.
4. The rash cleared in less than 48 hrs with the injection and some tablets ? Does ars rash clear this quickly ?
There is little reason to thing that your rash was the ARS. When the rash of ARS occurs it can be highly variable and typically lasts only a few days. The steroids you took are likely the reason your rash resolved, no matter what casued it/.
5. I read on internet the ars rash looks like hives (urticaria ) and I'm afraid the dermatologist misdiagnosed it. ?
See above, I would not worry about your rash
6. Please help me know risks of getting Hiv from receiving Unprotected oral ?
Again, see above
I hope these comments are helpful. I would not be worried about HIV and see no medical reason for testing. EWH