Please don't be worrying about visiting your GP when you receive something from DWP. It is only natural for a person with a condition that either causes disability or incapacity to keep their GP up to date with how their condition affects them.
Don't feel afraid that they would automatically assume that you are just trying to muster some support from your GP because you want to claim a certain benefit. I personally believe that it is right to keep your GP records updated with how a medical conditions impacts on you and your life. Use an appointment with your GP to do just that, give it to them in writing and ask for it to be held on your records. Lots of people with illnesses and disabilities are not regular attenders at their GP surgery, especially those suffering long term chronic conditions where little help can be offered and they find that they cope purely because of the way they manage their condition themselves at home etc.
So don't worry, lots of people have the same thoughts as you are having regarding this.