If your issue is psychological (which is quite likely), the only things that will fix this is time in the water, practice, and forcing yourself to be confident, calm, happy, and excited to do the dive. Your enjoyment of wanting to do the dive, and your persistence, will eventually wear down your inner worry, and you'll get over your fears. Jay has some good ideas.
If your issue is physical, (genuine lack of ability to breathe) then I recommend you do a few things:
1) Learn how to open the valve on your regulator to get more air from it. Sometimes if the regulator 2nd stage is partially or almost all the way closed, you wont get much air. Opening it allows a huge rush of air per breath.
2) Aside from doing #1, which is important, you also should be in good physical shape. Go running, hard swimming (above water, like freestyle or breast stroke etc) and also do some swimming where you just use your fins to kick very hard. Also, practicing with mask and snorkel in a pool will help you get used to the feeling while also greatly improving your cardio and leg endurance in the process. Also once a week, do some weightlifting for upper and lower body (2x a week if you are fit and ambitious). When you are in great shape, your body needs less air at rest or minimal activity, and you wont feel as fatigued or panicked from breathing out of the regulator.
3) Take full, deep breaths. If you feel the need to breathe fast, ok, breathe fast, BUT ONLY AFTER YOU HAVE INHALED ALL THE WAY AND EXHALED ALL THE WAY. This will get a ton of air deep into your lungs. Whatever you do though, don't hyperventilate by breathing shallow breaths rapidly. This is a bad idea, and it can deprive your lungs of oxygen. If you feel fear, just relax yourself and tell yourself "I am intelligent. I have a high IQ. I am in control of my dive. I will dive smart and be successful. Relax." Just be confident in your abilities, your training, and your body. And if your body is fat and out of shape (no offense of course), then getting into great shape before diving is certainly an ideal scenario (of course not everyone has the time in their day, or the ability to wait months to get in great shape, before diving).
As far as equalizing- make sure your sinuses are good (ENT doctor can tell you), sometimes people need one of the following surgeries to equalize properly- either A) deviated septum surgery, B) tonsil removal surgery, C) collapsed nasal valve surgery or D) polyp removal surgery. Sometimes, allergy shots combined with a corticosteroid nasal spray and a daily OTC allergy pill also help reduce inflammation of ear, nose and throat. If you are congested before the dive, mildly, then either dont dive or take a nasal decongestant like "severe cold and flu" 30 mins before the dive and combine that with a spray of corticosteroid nasal spray an hour before the dive. If you are very congested, then dont dive, period.
Equalizing should be done early and often, you should do it as soon as your entire head is under water, before you even descend further. If you are waiting until your ear hurts, then you are doing it wrong. You should do it before you feel really any pressure. It should be done every foot or two. If any, the feeling of ear/nose pressure should be tiny and manageable. It should go away each time you equalize.