OK lets think the worst has happened, you have got your enhanced DBS and the police have put a note on saying called to OPs address due to a disturbance.
That doesn't mean you cannot do the degree and work.
Most places will have a committee of some kind (others have other procedures) who will ask you about the circumstances and conduct a risk assessment.
You have to have an enhanced DBS, you don't have to have a clean DBS.
I know a teacher with an assault conviction, an actual conviction but she manged to get on a training course and find a job.
All of you saying, "It won't come up" it might, the police can add anything they think is relevant.
CRB (now DBS) was brought in after the Soham murders, Ian Huntley would (did) pass the old , "do you have an convictions spent or otherwise?" but under CRB/DBS information about the complaints made about rape and sex with underage girls would show up.
OP
Prepare for the worst, have a clear explanation, then if it doesn't come up you are fine and if it does you are a situation to state your case.
Until recently I have been teaching teenagers on BTEC health and social care, they have to have a DBS for their work placement. Until recent changes cautions for situations like yours were not uncommon.