The warmth and swelling concerns me, as it could indicate cellulitis, which it sounds like you're familiar with since you mentioned streaks, heat, etc.
It's good that it's draining, but I have to say I don't know what the chunky pieces are.
Is there redness? Is that redness spreading?
I used to work in public health, and we had a needle exchange, so I know IV users going to the ER is not easy, but is that a possibility for you? It sounds like you need an antibiotic, at least.
If that's not a possibility, here are some things you can do to treat it yourself - https://www.webmd.com/a-to-z-guides/abscess#1
Keeping it open and draining is really important. The bacteria is leaving as it drains. Don't try to close it up, or try to get it to drain faster.
If you get a fever, red streaks, it gets hotter to the touch, your arm swells more, you get dizzy or lightheaded, please go to the ER.
If there's a needle exchange near you, please use it.
We have a wonderful Addiction forum here. I'm linking it so you'll know it's here when/if you're ready - https://www.medhelp.org/forums/Addiction-Substance-Abuse/show/77
If you decide to go to the ER, let me know how it goes.