I have some doubts about both of the expressions you list.
Don't teach an old dog new tricks.
I haven't heard the old dog/new tricks expression used with this intent. Usually what people say is, "You can't teach an old dog new tricks." It means that someone is like an old dog, and that they are so set in their ways that they can't be flexible and adapt to a different way of doing things. I don't think you would apply this to yourself to indicate your expertise.
Don't teach your grandma how to suck eggs.
I haven't heard this one at all, so I may be completely wrong here. In that case, I'm sure others will let me know ASAP. I have heard the expression "to suck", though, and it's not good. My boss once tried to explain to me the saying, "That dog sucks eggs.", and it wasn't that good either. So unless I had a knowledgeable authority to vouch for the grandma sucking eggs idiom, I would be careful of it.
But for a positive contribution: the situation you describe is exactly what "mansplaining" is all about, except it only works when the advice is given by a male to a more experienced and aware female, so it may not work for your purpose.