Soooo hydrogen peroxide isn’t the greatest thing to wash wounds with... while it does Kill bacteria, it also kills your cells.
Iodine works better if you aren’t allergic to shellfish, then flush with lots of water.
The whole "shellfish allergy = allergy to iodine/iodinated contrast" is an urban myth. I deal with this daily. You literally cannot be allergic to iodine, as your thyroid requires it to keep you alive. Being allergic to shrimp or crabs just means you're allergic to shrimp or crabs. It is true that people with multiple (real) allergies have a greater chance of being allergic to something new, but that isn't that common.
The current medical standard is a chlorhexidine scrub (good ol' Hibiclens) unless documented allergic, in which case betadine (+/- followup isopropanol wipe down after drying) may be used. Killing a few of your own cells in a wound is not nearly as bad as leaving live bacteria in a deep puncture/wound. On the other hand, no need to go Rambo on yourself either. Wash with soap/Hibiclens, dry, neosporin to wound, cover with bandage, seek medical care if the wound is large/deep or the edges won't come together/you have specific concerns/you're immunocompromised or a poorly controlled diabetic/it won't stop bleeding.
Of note, the difference between an arterial injury and a venous injury is that veins ooze/slowly pour and arteries squirt (impressively). Treatment of both is to hold firm pressure until the bleeding stops (preferably with a hemostatic device like a QuikClot). For a vein injury, this could be 5-10 minutes (usually less, barring anticoagulation). For an arterial injury, 10-20 minutes for small vessels and "until you go to surgery" for anything bigger. A 1 mm artery will bleed you out in roughly 40-50 minutes if nothing is done to stop it. Bigger vessels will take substantially less time. If you are on anticoagulation of any sort, you must maintain pressure on the wound until you are seen by a trained medical professional for anything larger than a scrape.
Weird punctures (especially from anything marine/ocean based) probably require medical care immediately. Mycobacterium marinum can create nasty problems for you. Other seemingly benign things like rose thorn punctures can have weird infections (Sporothrix) that definitely require medical attention. No one will laugh at you for having your wound checked at the doctors office and it may just save your life.
Mike