A "a bruised and swollen lip" doesn't sound that significant... may take a week or two to recover at most, right? If that's your first and worst injury after 6 months training, it sounds like the general safety level is quite high. The kinds of things to ask yourself:
How often and significantly do you see other students injured during training?
Have you noticed other students nervous when there's sparring, or dropping out from classes?
Do any people who're getting injured or sparring with an intensity clearly more at risk of injury seem to be paired with equally willing and skilled participants in harder training, rather than reluctant or weaker training partners?
Does the teacher lead into sparring in a way that doesn't get the participants too hyped up, e.g. perhaps by having an initial round of light sparring, or giving students specific skills to concentrate on during the practice?
Do the senior/stronger students generally encourage you even while challenging you during sparring?
Looking back on how you got hit, what's your understanding of how it happened?
Do you think the attacker was excessively, persistently aggressive, careless, or casually indifferent to hitting you?
Was your blocking or dodging flawed in a way they didn't anticipate and reasonably failed to compensate for?
Did the attacker seem concerned when you'd been hit?
Do you believe they'd be extra careful not to hit you again?
Do you believe you could defend against similar attacks more successfully next time? (Are there related skills you could drill with a training partner you trust so you're better prepared?)
My question is whether I should talk to my sensei about wearing gloves during sparring? I'm a beginner student so I'm hesitant to tell him how to conduct practice. Are gloves always used in sparring? How typical is it to spar without gloves? How should I talk to him about this?
If the frequency and seriousness of injuries is low, your instructor may well think having everyone wearing gloves all the time is an excessive measure. They may be unimpressed by the suggestion that gloves are necessary, but that doesn't mean you can't or shouldn't ask.
On the other hand, if injuries are common, you may be better off finding another dojo.
Personally, I'd say the threshold for protective gear in children's classes should be dramatically lower - kids don't have the concentration to practice as safely, and are more easily injured.
An alternative is asking if you can wear a mouth guard - that's a less intrusive option, and doesn't require any involvement from your training partners. If it's really important to you, you could even say your dentist has recommended it because a tooth is loose, or something like that - then if the instructor forbids it you really should find another dojo as there's no excuse for asking a student to ignore medical advice (unless known to be fake O_o).
That said, part of learning a martial art is gaining some perspective on injuries - being prepared to accept some risk and realising the kinds of injuries that're completely healed within even a few-month timeframe can come and go many times over decades of training.
I trained for a couple decades in half a dozen styles before joining kyokushin, and it's my first time wearing gloves and shin guards, but countering the safety aspects of that there's considerably more contact. I've broken a few bones (all but once by kicking elbows or the heavy bag) and had some bruising that took weeks to recover, but nothing I regret: it's all just history now, and I value the experience of training, and progress, far more.
