Whatever else you do, I would start looking at care homes ASAP. You may have to look at several before you find one that feels right, and many of them have waiting lists.
Putting her name down would almost certainly not commit you, though - there will usually be someone else waiting.
If your mum would be self funded you do not need to involve social services, although some people prefer to anyway. We arranged care homes for both my mother and my FIL on our own. I won't pretend there wasn't an awful lot of looking both times, though.
One thing I would say, cross off any home that asks you to make an appointment just for an initial look around. Any good care home should be happy for you to drop in at any reasonable hour, though it's best to avoid mealtimes, when staff are often particularly busy.
If your mum does not already get Attendance Allowance, be sure to apply for that ASAP. If she is self funded it will continue to be paid while she's in the CH. Its a bit of a drop in the ocean compared to fees, but every little helps.
Good luck - it can be such a worrying and difficult time.