I have a mole on my back 7mm wide and it has a lump grown within the mole. My mum died of melanoma. Should I be worried?

Probably. I can't see the lesion you are describing, but until you have it biopsied or seen by a dermatologist, I wouldn't feel comfortable until I did.
Melanoma. No need to worry. Worry never helps with anything. Have it looked at by your primary care doctor or dermatologist. With a family history of melanoma, you should get regular skin surveys by a dermatologist.