Thanks for using JustAnswer.com, I'm Dr. Dan and I'll try to help you.
If a tick's head is still embedded in your cat's skin it is not a very big deal. Your cat's body will reject the tick's head with pus just like an infection. Unless the area becomes really large or has a large draining sore then a vet visit will likely not be needed unless you are really concerned. Your cat's body will take care of it on it's own.
I hope this helps, best wishes.
The straight line is likely the stinger so I would guess you have the entire tick so you shouldn't have to worry. It is not unusual to have the area become thickened like a mosquito bite however in reaction to the stinger.
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