Using dummy variables/interactions in a regression and possible problem of overfitting

I have three type of dummy variables (hours, weekdays, months). Using those dummy variables as interactions in a form
creates around 2000 variables (although p-values for most of them are significant).

I am worried regarding overfitting and what other approach I could use? If I use
I get less variables, but also less Adjusted R2 and also RSME.