Hello and welcome to HCM
You have mentioned that there is a bump on a shoulder with a black dot in the centre.
On the basis of description this lesion appears to a lesion known as 'sebaceous cyst'
This type of cyst is formed by blockage of opening of sebaceous gland
The cyst is filled with a substance known as keratin.
The pus like material which is expressing out is keratin.
Treatment of sebaceous cyst is surgical removal.
After removal the cyst should be sent for histopathological examination.
I hope my answer is of help to you.
Thanks and take care
Dr Shailja P Wahal