If you need to keep a bigger logo ( I see that you reduced the size of the logo at present and things look fine), you can control it’s size by inserting the following code into Custom CSS to limit it’s using CSS –
#site-logo { max-width: 250px; } /* Height of logo adjusts automatically */
and
#primary-menu { margin-right: 100px; } /* Set lesser margin if you have only couple of social icons */
Pls vary these values based on your exact space requirement for logo on the left and social icons on the right. It’s hard for me to know how many social links/icons someone will want to have in their header. Thanks