Injecting a tiny amount of air is not the worst thing you can do while injecting, many IVers painstakingly make sure they get every last tiny bubble out as if their life depended on it (probably think this via junkie lore, which is totally untrue) whilst totally neglecting far more important sanitary requirements such as using a fresh rig each time, using a clean cooker and distilled water, cleaning the site of injection with an alcohol swab first, etc. (hopefully you are doing as many of these things as possible). To be clear, in order to kill yourself with air you would need to inject quite a lot, my paramedic friend said he was told 1ml of air would be enough to kill somebody (that's a full insulin syringe). To be safe I'd reduce this to 0.25ml, but a little bubble? Not much of a concern though I still feel it's a good idea to get it out before trying to register again (what's the harm, right?).
If you have shot into an artery, you will know! It will hurt very bad in your hand/wrist (if you are injecting into your arm). The trick is to not ever hit an artery because it is not only very painful, but very, very dangerous! Arteries tend to be much deeper than veins as they are far more vital, you wouldn't want to be dying from scraping your arm so evolution has taken care of this for us, luckily. But once veins near the surface become more scarce people find themselves digging. If you have visible veins they appear green, sometimes blue-ish and are just below the skin (sometimes bulge out in some areas if you're lucky as I am). Arteries would appear red or pink if you could see them, but you shouldn't be able to see an artery. So always try to stay as close to the skin surface as possible when choosing a vein and injecting, don't go digging. I've also heard that if you are in an artery, and when you pull back, instead of the blood coming in as a smooth red streak and somewhat thick it will be more pinkish and bubbly. If your blood comes in looking like this, definitely don't inject as you're almost certainly in an artery (luckily I've never been able to confirm or deny this as I've never so much as registered in an artery, let alone inject into one).
Finally, be safe and read as much as you can. Try not to miss any shots, it's a real pain, I've only IVed 20 or so times, and I've missed twice. Not a track record I'm proud of, lol. But I become very impatient and don't like poking myself with needles plus I always register the first time (and even when I've missed I've registered, but have only been just in I suppose) so this makes me a bit over-confident and if I register at all I declare myself in and go for it. If it is harder than usual to push down the plunger, don't hesitate to remove the syringe and re-register. It will save you a lot of grief being patient (and you'll get a good rush every time, no rush when you miss a shot). If you do miss you'll know as there will be no rush, the area will feel a bit burning/stinging and sensitive, warmer than normal and probably have some lump bigger than normal. Immediately put some Polysporin on (you should be doing this everytime to help heal your tracks anyways and avoid complications) and give it a damn good massage. If lucky you will still get a fairly good buzz from the IM injection if you're massaging hard enough. After 20 minutes of good massaging apply heat for 30 minutes and do this 3-4 times a day until things have cleared up. Also apply Polysporin 2-3 times a day and massage the area. If you develop a hard lump under the skin which sticks around for several days, or if your arm still hurts after 4-7 days get yourself to a clinic or the hospital (this depends on severity of pain and if you perceive it as getting better with each day, if things are improving and there's less pain each day then hold off, but if there's no improvement or things are getting worse then don't hesitate, abscesses can be very dangerous if left untreated for too long and get badly infected).
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