Benzyl Alcohol is why you can get quite sore after a quad IM. For whatever reason, in that particular site, that alcohol likes to separate itself out from the oil and migrate towards your knee (and this is the only injection site that will do it almost every time). Alcohol, of course, is an irritant to all tissues and that is why it feels so uncomfortable or irritated (slightly inflamed even).
Also, virgin muscles don't like having their tissues displaced to receive what is essentially a sterile abscess (the T and oil balloons the muscle tissues a bit and it stays like that, just like an abscess -sterile- , until your muscle's metabolic activity breaks it down until it is all absorbed).
It gets better. And for when you eventually start self-injections, DO aim for the Vastus Lateralis in your quads, always. Try your absolute best to get it closer to the center (as in between your knee and hip, center, not center of the leg towards or away from your nethers), as that is where it is at its widest and thickest and NOT to go too deep (it is not necessary, in most people, to sink it all the way) or too shallow either (about half-way of a 1-1/2" will suffice), because it really hurts to have it balloned in not enough muscle or, worst of all, between two muscles. If you don't get it in the ballpark on any of those, well it'll be worse.
For me personally, I can't do the "dart" motion with my syringes in that area. I tell my brain to do it, I'm determined to do it, but something just stops me every time (it's infuriating). So, instead, I have to do it with the significantly less comfortable method of putting the needle flush to where I want it to go and then 'shove' it in. Feels spectacular.
Anyway, if you get it in the "sweet spot", you won't feel anything after the initial stick. My last shot in the quad was perfect, didn't even have the alcohol migrate or anything.
Oh and, IMHO, gluteal IM's are by far better. I personally don't feel a thing there. So if you can, someone else doing it in that area is best. Unless you'd rather do it on your own, that's fine too, it's just not as comfortable and painless.