So if you can explain more about your free-tier, I can edit my response later. For now, I will explain for both options. You can find free services from here. You will need IBM Cloud Cli tool which can be downloaded:
First account type is: The lite account. In this option, you cannot create IBM Kubernetes service or OpenShift cluster. You can only access to some lite services (apprx. 40 services) and one of them is Cloud Foundry Public. IBM Cloud let you use 256 MB of RAM on Cloud Foundry Public with free of charge. You can use the following command:
ibmcloud cf push \
--docker-image <your-image> \
--docker-username <your-username> \
--random-route \
-i 1 \
-m <memory_limit_max_256_mb>
You can find more details by writing ibmcloud cf push --help
Second account type is: trial/free-tier account which can be had by two ways: a feature code or switching to pay-as-you-go.
This option includes the Cloud Foundry Public also, I won't repeat it. But with this account type, you will have IBM Kubernetes Service Free (Deletes itself 30 days later, you can create one more after that time)
When you create a kubernetes cluster on IBM Cloud, you will see the service page. There is an access menu on left tab-menu. You have to follow those steps to be able to access to your kubernetes cluster from your workspace.
Then it is easy to deploy your image by entering:
kubectl create deployment app --image=<your_image_url>
If your image is not publicly accessible, then you have to create an imagepullsecret and bind it to your service account but this is out-of-topic. You can find it in here