I had real problems with my son at 8 months and had a woman who specialized in babies and behavior come and give me advice. It worked beautifully, and made everything seem so simple. So, this is what she would have said to you:
Ensure you have a good daily routine. I assume your 7 month old has begun on solids now. Start feeding with solids, keep spooning the food in until it literally will come back out or you cannot get any more in. That means he's full. Follow with milk or breast about 1/2 hour later.
He probably does still need a nap. Look for tired signs, cartoon style; rubbing the eyes, yawning etc. Once you recognize them its hard to ignore. AS SOON as you see he's tired, put him into bed for a nap. This should be shortly after lunch, and so he should not be hungry. You'll get the timing of this right eventually! Put him down with a clean dry nappy. If he cries, leave him. He's crying because he's tired and needs sleep, he has to learn to go to sleep without help.
Make sure he has a good dinner, evening routine and put him to bed probably around 7pm or so. If he wakes in the night, you can go in to check he's ok, tell him its night and time to sleep and leave him. If you play with him you are teaching him to wake up more easily.
When children become overtired it actually is more difficult for them to fall asleep. You have a short window of opportunity (about 20mins for a 7month old) in which to ensure the nappy is clean and dry, and get them into bed for sleep, either at nap time or for a night sleep. If they have a good routine and plenty of good food they are totally capable of sleeping through the night, even while teething. Waking is not a habit you want them to get into, nor encourage as they need plenty of sleep for good health.
If this sounds really old fashioned, it is. But this approach totally worked for me. Our days became like clockwork, and nights peaceful. He was happy and healthy.
It takes 3 days for a habit to be broken, so you can expect 3 days and nights of battle. Maybe up to a week. If you are committed and strong you can have a great outcome.
If you think there may be a medical reason why he's suddenly not sleeping see a doctor. If the doctor gives him the all clear, then its just a habit, maybe precipitated by the teething.
I hope this helps. Good luck with whatever you choose to do!