If I have a call option and exercise it today will I be able to receive the shares immediately to sell them?
When you will have shares in your account after you exercise will depend on how timely your broker processes and handles exercise.
At my broker, the moment I click 'Exercise', the transaction occurs immediately and either the short shares disappear from my account or the long shares are now there. This is reflected immediately on my Accounts Summary page. In the case of share acquisition (not closing a short position), I have never had an issue with selling these newly acquired shares shortly thereafter.
Note that settlement is T+2 so my broker is effectively providing shares to me, likely from another in-house account (assignment and exercise notifications are handled by the OCC after the market closes), unless this is considered an exception to a hard to borrow share situation.