If your Mum is willing to pay for it, I'd accept the opportunity.
It doesn't mean anything is wrong with you.
Counselling is extremely expensive and quite a luxury -
at the very least it's the chance to talk about your grievances
to someone who won't judge you.
There are many kinds of therapy. All are forms of personal growth.
You could research the various types and see if any appeal to you.
One place to research is the free online magazine. Psychology Today.
Some therapists are ineffective; some are nearing burnout.
If you feel empathy from the counsellor and a sense of rapport by the end of the first session, then that's the person to see. If you don't, be patient and see others until you find one with whom you click.
A counsellor can help give you some coping strategies,
and find a way to deal with the difficult emotions that inevitably arise
when living with a drinker.
Another alternative is attending CoDA (Codependents An, onymous) or Al-Anon. These are 12-step programs, free to attend, run by volunteers, and almost everywhere. You could find your nearest group online.
It can be a way to talk about things without any judgement from others,
and can provide a pathway to personal growth.
If you can find a way to move out,
perhaps into a rented share house with other young singles,
that would be ideal.