It looks like a zit. But I have had it about 3 months now. A skin growth is what I call it. If I try to pick at it, it will bleed. So I leave it alone and keep my face washed and put lotion on it.
How do I get rid of it? Is this a matter for a doctor to take care of?

You may want to let a dermatologist take a look at it.

I and most of my family have every kind of skin growth there is, from harmless tags and fatty (sebaceous) moles to basal cells and melanomas.
Causing it to bleed is not a good idea.
Yes, wash it of course, but mainly stop picking at it. I'd also cover it from sunlight til it can be seen.
See a dermatologist.
I have a pink basal cell that NO ONE thought was one until the lab results came back positive. I wondered because it started out as a mosquito bite 5 years ago, but grew wider.
Big 'tags' are usually pendulous (sort of hanging) and are harmless. So are big fat moles, as long as they are uniform.
It takes years of study to recognize differences.
Basal cell cancers don't spread except their surrounding area. Melanomas, VERY different kind of cancer, spread internally and can be deadly.