Not all babies, sleep through the night by now. MOST babies don't. I think it's a real "myth" that people and books will tell you that a baby "has to " sleep through the night by 6 months of age... it just stresses parents out.
Each baby is different & has their own pattern... many babies don't sleep through the night, and in fact, many children don't sleep through the night until about 2 years old.
Also, there are developmental & cognitive changes & growth spurts which also tweak a baby's slumber and wakes them. This is normal and common. You can't really "avoid" their developmental changes/sleep changes.....sleep patterns are NOT static...they ebb and flow and change as a baby changes. BUT...you can get a baby into a routine....meaning consistency in sleep/nap times and pre-sleep routines to get them in the patterns of good sleep habits....so that down the road as they get older....they will be on a good pattern of sleep times and habits.
If his sleep is being interrupted because of teething...well, you can't "make" him sleep and not wake up...teething can be painful for them. Many Moms sleep with their child in the middle of the night because this helps them to go back to sleep AND it's tiring waking up in the middle of the night. But, well, this is how it is. I did that too, with both of my children and still do, if that is what they need. I have not slept through the night myself, for the past 6 years. LOL. Oh well.
Personally, I do not like the CIO method. I preferred to get up and comfort or feed my babies if that is what they needed. Especially during a growth spurt...they get hungrier, and more often and need to feed more frequently. So that is what I did even if it meant waking up in the middle of the night. Basically, the CIO method works because crying and crying tires a baby out...and then they get so tired from crying that they pass out. And, they "realize" Mommy is not going to come and help them, so they basically give up, then stop crying, and fall asleep. It's behavioral modification. Not, natural patterning.
I know it's tiring waking up. But well, they will not be babies for very long, they grow up so fast and soon will not need you at night. Enjoy this moment, as it is just their developmental phases. They don't do it on purpose.
For teething, the "Hyland's teething tabs" or drops are great. It's homeopathic. Or try Tylenol, per your Doctor's dosage recommendation.
My son was a voracious feeder, even at night. So with him, I woke up and nursed him if that is what he needed.
ALSO though, I did not get up for every little noise or cry that he made.... I listened carefully, and I could tell by the pitch of his cry, or the kind of crying that he did....whether or not I had to get up to help him. Often times, he could go back to sleep himself... if you just give them a moment. Also, a baby will often make noises during sleep, or sort of "wake" momentarily....it is a transitional waking as they segue into more deeper REM sleep. So, you MAY not have to swoop in and get them/pick them up for every little noise they make. See if they can self-soothe first.
Also, you may try giving him a "transitional object" to sleep with. My boy, since he was 6 months old, started to get attached to a stuffed cow... and we found it helped him to self-soothe and fall asleep. It's very good that he could "problem solve" and found that this cow helped him and he finds it soothing. It's his best "friend" and he likes to carry it everywhere, which is fine. It's normal.
Every baby is different. "Sleeping through the night", for a baby, means sleeping at least 6 hours straight. SO, with that in mind, I think your baby does that quite often. Remember that "sleeping through the night" is not by "Adult" standards...it's per a baby's age. Your baby also seems to nap fine. That is great! But now with his teething, it wakes him. That is just a phase. It's normal and it is just for now. Just KEEP up with his sleep routine and sleep times....keep it the same, since consistency is important. That's what I did and as the phase passes, they will go back to their more normal sleep patterns...even if it is not always what we want. Each baby has their own pattern. Yes, as they get older...they tend to sleep for longer stretches...generally. But, sometimes that will not happen until they are much older. My firstborn did not do that until she was about 2 years old. My second born, now 21 months old....is now sleeping most of the night without waking. BUT, he sometimes still wakes up once a night....and he can mostly put himself back to sleep by now.
Sorry for rambling. Just some thoughts, I'm trying to type fast as I need to get my son to nap now! Good luck and all the best,
~Susan