An empty phone gallery does not prove that your Google account has room for another email. Start with the account named in Gmail's storage warning. On a shared computer, check the profile picture before removing anything: you may be looking at a different mailbox from the one that stopped receiving messages.
Find the space that actually matters
Gmail shares account storage with other Google services. When the limit is reached, incoming mail can be returned to the sender. Deleting a downloaded attachment from your laptop therefore does not solve an account quota problem.
Look at the storage breakdown before choosing files to remove. Perhaps a few old videos occupy far more space than years of short emails. This is a reason to inspect them, not permission to erase everything in that category. Keep an independent copy of anything you still need and open that copy before deleting its original.
Items in Gmail's Trash and Spam still count. Review them before permanent deletion; do not empty them blindly while also searching for a missing message. Storage totals can take time to update after cleanup. For a work or school account, ask the administrator about its allocation if the limit remains unclear.
Check delivery, then recover the gap
Once the quota shows available space, send a small test from another account you control or ask someone to help. Check that it arrives in the intended mailbox. Record the approximate period when storage was full.
Suppose an appointment confirmation was sent during that period. A successful test today does not prove that yesterday's confirmation will arrive automatically. Ask the sender to check its delivery result and resend the message if needed. If fresh mail arrives but one older message remains missing, investigate that message separately, including Spam and Trash, rather than deleting more data.