Hi, thanks for using healthcare magic
It is understandable that you are concerned.
The incubation period
which is time from contact with a disease to the time the symptoms present, varies but is usually 2 to 12 weeks. In some persons it may be from 4 days. During the incubation period there are no symptoms.
You stated that your symptoms started from the time you were biten which I take as meaning almost immediately,in that case rabies
is unlikely because there is the incubation period mentioned.
The fact the there was no blood contact also reduces the chances.
and cold may be the common cold
You can consider consulting your doctor if you remain concerned.
I hope this helps