Using CIVICRM API can I get both mobile and phone number?
you can get both Phone and Mobile in a single API call as below 

    $result = civicrm_api3('Phone', 'get', [
  'sequential' =&gt; 1,
  'contact_id' =&gt; 203,
  'phone_type_id' =&gt; ['IN' =&gt; ["Phone", "Mobile"]],
]);


I have created the test example against https://dmaster.demo.civicrm.org

I guess this helps !!!

Thanks