As long as you keep to yourself and just be aware of your surroundings at night you’ll be fine. If it’ll make you feel a bit safer you could carry a pocket pepper spray on your keychain (I have one and never had to use it). Give it a month and you’ll get used to the area and get a feel of how the neighborhood is.

There are many posts in this sub on where to find certain foods, nightlife, etc. that I think you’d find useful. Good luck and welcome to Worcester!