Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand..
As per your complain it seems like severe infection at the site of 
spider bite and along with infection there is also prevailing 
allergic reaction to the toxin present in spider sting..
You are taking a correct line of treatment as it looks like an abscess and not staph infection..
You should continue taking the antibiotics and painkillers advised to you as well as keep doing the dressing by cleaning with antiseptic solution and apply 
triple antibiotic and steroid ointment at the bite site..
You can also take anti allergics like Levocetrizine..
Streaking seems to be due to inflammation..
In case if you do not find improvement or symptoms become exaggerated 
consult a general surgeon and he can give you injectable antibiotics and 
steroids for faster relief..
Hope this information helps..
Thanks and regards.
Dr.Honey Nandwani Arora.