Before I even start: Ask a doctor. That's what doctors are for.
Depression can roughly be divided into two types, usually intertwined with each other: chemical and psychological. If your brain chemistry is off and you don't get enough serotonin or any other form of chemical you desperately need to experience and retain positive emotions, there's no form of therapy that will help you. You will need to find a medical solution that might involve eating pills for a long time. That said (and I'm no expert, I'm just quoting one as well as I can) the right kind of medication allows for plasticity in your brain, in other words it makes it easier for your brain to learn new working patterns.
I know a little bit about hypnosis, mostly about what it's commonly used for and what the general limits are. One major limit is that it requires 1) that you trust the professional performing the treatment, 2) that you are the part of the population that knows how to be hypnotized. The second part will sound extremely weird and requires some explaining. What hypnosis is at its core is a person allowing some of your conscious thinking and limitations to give in to what's deeper under the surface. A hypnotist can introduce you new ideas (known as suggestions), but you still need to accept those ideas yourself. You do all the work. Not all people are naturally as good at relaxing and entering what's called the trance state (which, by the way, is horribly misrepresented by popular culture). If you lack some of the necessary traits you can learn to become better at being hypnotized, but it doesn't automatically have the same effect on everyone.
Suggestions on the other hand are quite aptly named, since they're just that. If your mind accepts a suggestion, consciously or subconsciously, it will introduce a new kind of thinking to you. Typically these are tied to certain situations and certain reactions, where the treatment is directed towards making a stop to faulty thought patterns, like addictions or fears. For example a hypnotist could introduce a kind of safety mechanism for especially stressful situations, where a certain gesture (like closing your thumb into your fist) is equated with a certain emotional state (safety). Hypnosis is good at these kind of specific state changes as well as for safely approaching emotionally volatile situations or memories.
Which brings up a very important thing. Do NOT EVER go to a hypnotist to treat traumas or depression stemming from your past if you're not absolutely sure they will work ethically and in a respective manner. Hypnosis also has the power to create false memories. If a hypnotist ever starts asking you questions that seem to push you in a certain direction (the classical "did your father abuse you as a child?" "no" "what did he do to you?" type of conversation), get out immediately and find a new one. If you have a rough past, a regular therapist will be able to talk to you about it in a safe manner. Finding a therapist who chimes with you personally and who you feel safe with however requires a lot of work and you should not stop looking after it didn't work out with the first person.
So what would hypnosis do if you are depressed? Well, it should be obviously by now that it depends on your form of depression and where it stems from. Hypnotherapists work to give you conscious shortcuts to solve emotional problems. If your depression is not constant they can provide you with tools that mitigates the emotional stress in given situations. They can (and usually do) teach you how to use self-hypnosis to come over rough patches where you need all of your available energy. If you're dealing with these kinds of problems, hypnosis might be the thing for you. The best way to know is to ask an actual hypnotist.
Personally, if you're the type of person who feels drawn to hypnosis, I recommend getting familiar with visualization techniques. A mix of visualization and mindfulness meditation works for many people and it's possible to learn them on your own. What should be remembered however is that if you have any sort of traumas or anxiety, you shouldn't begin practising these alone. Make sure that you have an emotionally safe setting you can fall back on if the things your mind provides you during meditation disturb you or worsen your depression.
To finish with the most important thing and repeat it once more: consult a medical expert and work carefully through your individual situation. No amount of knowledge or help from the web is going to provide you with everything you need.
