First of all, I would like to inform you that normally it takes 30-45 days for any form submitted with the institute to be processed and confirmation/acknowledgement letter to be dispatched by the institute.
As far as articleship registration is concerned it can extend upto 2 months also.
Further, I would also like to inform you that in Kolkata, Institute has shifted its office for students/articleship registration section to a new location. All the work of institute has been disturbed.
Kindly let me know your location and Unique Registration No so that details can be shared with you.
U can call regional office of your area, tell them your details and get all the required information.
Further, as u said that you have joined for articleship in a firm from 22 JUN and has sent form 103 along with all the relevant documents on 2nd of july. You should be informed that the date of articleship starting date as mentioned in point no. 11 of Form No. 103 is applicable irrespective of the date of exeuction of the deed or submission of the form with institute or date on which franking is done.
You can call student toll no. 18002002500 of the ICAI for any other detail.