I don't have a computer to use to reset it and when I hold the power and home buttons down it restarts and still asks for the passcode.
Will hard resetting my phone solve this? If not, what can I do?
If you have forgotten your passcode, the only option available to you is to erase your iPhone and start again. Unfortunately, if you haven't got a backup of your data, this will mean you will lose any data you haven't already got saved somewhere. However, on the positive side, any purchases (free and paid) using your Apple ID will still be intact as you can sign in again and redownload them.
While the only option is to erase your iPhone, you do have multiple methods of doing so. I recommend you read If you forgot the passcode for your iPhone, iPad, or iPod touch, or your device is disabled.
The above Apple support document will explain your options, including how to restore any data you do have backed up.