Spider fangs are stuck in my flesh?

So I just came back from a camp in the bush. I was on a train when I felt a sharp pain near my neck. Right when I felt it, I pressed on the place in which the pain came from in hope of killing what had bitten me. I pressed as hard as I could for 10 minutes and lifted my hand away to see a squashed small crab-like spider. I thought it was dead seeing the state of it, but when I tried lifting it off, it wouldn't come off, and instead its legs began unfolding and moving. I was so scared I pressed onto it again, this time harder and for say, 2 hours. During this time, I had tried sliding it off my skin, but it wouldn't budge! So in the end, whilst pressing onto the lower parts of the spider, I cut its fangs from its body. I ended up throwing the body away, and had fangs stuck in my flesh. It is a little red around the fang marks and it hurts when I touch it. Is it safe to leave it there? Will it break down somehow? Or do I need to remove it and how?
Spider fangs are stuck in my flesh?
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