Use this command in an sql-interactive-mode buffer to open a connected sql-mode buffer, in which you can edit queries to send to the database process (check C-h m for the keybindings to do that).

 (defvar my-sql-query-buffer)
 (defun my-sql-query-buffer (arg)
   "Open a `sql-mode' buffer which interacts with the current SQLi buffer.
 Switches to an existing buffer if possible, otherwise creates a new buffer.
 With C-u prefix arg, always creates a new buffer."
   (interactive "P")
   (let ((sqlibuf (current-buffer)))
     (if (null (sql-buffer-live-p sqlibuf))
         (error "Buffer %s is not a working SQLi buffer" sqlibuf)
       (let ((product sql-product)
              (or (and (not (consp arg)) ;; prefix arg
                       (boundp 'my-sql-query-buffer)
                       (buffer-live-p (get-buffer my-sql-query-buffer))
                       (get-buffer my-sql-query-buffer))
                   (format "*SQL ctl: %s*" (buffer-name sqlibuf))))))
         (setq-local my-sql-query-buffer querybuf)
         (pop-to-buffer querybuf '(display-buffer-reuse-window
                                   . ((reusable-frames . visible))))
         (unless (eq major-mode 'sql-mode)
           (setq sql-product product)
           (setq sql-buffer sqlibuf)
           (run-hooks 'sql-set-sqli-hook))))))
 (eval-after-load "sql"
   '(define-key sql-interactive-mode-map (kbd "C-c q") 'my-sql-query-buffer))

Note that you can do the reverse by default – from a sql-mode buffer with the appropriate selected product, use C-c TAB to create the connected sql-interactive-mode buffer, and start an interactive session. You can use a prefix argument to also select the product for the interactive session, but it’s better to choose it for the sql-mode buffer using the menus: M-` s p