At the moment, aside from hot compress there is little to be done unless you are feeling systemically unwell. There is a risk that this will develop into an abscess and so you need to keep an eye on the area for swelling, heat and pain.
In that case then you would need to see a doctor for possibly antibiotics or even drainage if there is a fluid collection under the skin.
We would recommend that you no longer use injections as a form of self-treatment. The potential for infection and blood clots is high. I have seen people lose a leg because they injected into the groin and developed an infection that spread.
If it is now a couple of days then stop the hot compress and observe. The fact that it is now red suggests that it may be brewing an infection. You should see a doctor for an examination in person.
I suspect that you may now need antibiotics, although the redness may be a response to the irritation of the injection ingredient under the skin.
Only time will tell what damage you have done. The contents of the injection will be irritating to the tissue, and may cause a local inflammation which is not infected. So it needs a clinical assessment.
I would not recommend you self treat, doxycycline is not my first choice for skin infections, Usually a high dose flucloxacillin is prescribed. If the infection is deep,or an abscess then you may need intravenous antibiotics.
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