Will I be able to create search profile?

Yes, it is possible to create search profile that can be published for all users or for only the users who has created the profile. Click the ‘Default Search Profile’ button and select a search profile to make it as default. When you make a search profile as default, the search profile is applied to the request listing page when you login (in this case ‘All Incidents’ and ‘My Incidents’ tab). The search profile selected as default will have a tick mark in the ‘Default Profile’ column as shown below. Please refer help link Custom Views for the configuration.