The starting point is that generally images / photos are protected by copyright.
With regard to images you’ve created, there is no issue as you would own the copyright.
With regard to images you’ve purchased from image libraries, then again there is no issue as you will have purchased a licence to use the image. However, you will need to take care to check the terms of the licence as your use of the image may be restricted and you will need to ensure that you use the image only in accordance with the licence, to avoid having to pay additional fees.
With regard to images you source via Google Images – or elsewhere on the internet – you will generally need permission to use the image. The fact that an image is posted on the internet does not mean that the owner has ‘waived’ or lost the copyright in the image or given permission for everyone to use it. If you use an image without permission, while the owner may never find out, there is a risk that if the owner does discover it they could claim compensation (based on a reasonable licence fee plus costs etc.) from you. Image libraries and online publishers use sophisticated technology to track the use of their images / content and then aggressively claim compensation for unlawful use.
If you post an image on to a social media site without permission of the image owner, then this will also breach the T&Cs of the social media site as usually the T&Cs require that you do not post any infringing material. They have the right and obligation to ‘take down’ content that infringes third party rights.
Some websites allow their images to be used under a “creative commons” licence. However, often this is only for non-commercial use, so it’s important to check the licence terms if using Creative Commons-licensed material.
Sharing a simple web link to an image is usually okay because in that case you have not made your own copy of the image, you have simply linked to the image on another site. However, this can be an issue if the result is to circumvent a paywall or other subscription only services. You may also infringe copyright if you use image tags to insert images hosted elsewhere into your webpage (even without copying and hosting the images yourself). Again, this is more likely if the original images are posted behind a pay wall or in some other restricted access environment. So using links is potentially risky as well.
You can use copyright works without permission from the copyright owner for certain specific acts, known as ‘fair dealing’. This will include use for ‘research for a non-commercial purpose and private study’ or for ‘criticism and review’ (e.g. if you write a blog post about how effective or creative a particular image is, then that would be criticism or review of the image itself and would be covered by fair dealing). In such cases you have to give a sufficient acknowledgement to the owner.
Using pics of celebs can give rise to other issues as they may be able to claim that their privacy has been infringed or that your use of their image wrongly implies that they have endorsed your product or service.