No red flags. They are required to fill out some reports if a deposit is $10,000 or more. But even that isn't such a big deal. People get insurance settlements, etc for that kind of money all the time. They fill out the form and 99% of the time - it's no big deal. The red flags come up if someone is depositing this kind of money every week or so and there is no good reason for it - such as 401k money or insurance settlement money. The red flags come up with the government if someone is depositing large amounts of cash regularly for no good reason - like business deposits - as it can be a red flag for money laundering.
This may be a fairly large amount of money to you - and I'm not belittling it - but it is not a fairly large amount of money for the bank or the government to worry about.
You will be fine.
Banks are used to varying amounts of deposits from businesses and customers. That is the nature of their business, to deal with customers from all walks of life. .
$3K should be fine - only kicks in around $10K. But do deposit it. Keeping physical cash around is a very bad idea. If someone broke in to your place, or there was a house fire, etc. you'd be out $3k.
It is your own money and invest as you like, If you are prepared to take risk you may invest in stock to earn good income. It is safe to invest in banks, but the rate of interest is very less.
I wouldn't worry too much about it. You aren't doing anything illegal. Just tell them the truth if they ask.
No red flags there.