You can regain access to your account by initiating the account recovery process. Here are the steps I got from Apple Support.
1. Go to iForgot.apple.com
2. Enter your appleID and click on continue
3. Enter your old phone number and click on continue
4. It's going to ask you to look for the notification it sends, but underneath you will select the option, "Don't have access to any of your devices" that is in blue letters.
5. On the bottom of the next page (in blue letters) will be, "Can't get to another device". Click on this.
6. It's going to explain account recovery to you, then click on "Continue anyway"
7. It's going to ask you to enter the code sent to your number. Click on "Don't use this number anymore" written in blue letters underneath
8. Enter your new number, select whether you want to receive a text message or phone call, then click "Continue"
9. Enter your verification code and then click "Continue"
10. It's going to ask you some information regarding your account, then it's going to give you a time frame on how long it will take to evaluate your account information. Once that time is up, you will receive either a call or text with information regarding how to regain access to your account.