I woke up itching and had been getting bitten but no visible signs of bed bugs. Could it still be bed bugs?

Yes. Bed bug bites may cause no symptoms or signs in some people. When there is a reaction, it may not show until several days after the bed bug has bitten. It can cause pink, itchy, swollen lesions on the skin. What can be telltale is when there is a linear track of lesions from sequential feedings – but that does not always occur.
Yes. It takes time for the bugs(who burrow under your skin) to activate your immune response.History is important;have you slept where you could have been exposed?If so you may benefit from treatment for these unpleasant bugs.