Remember, fasting is a tool used to get closer to God, and it actually should keep us from being preoccupied with food. If your method of fasting is going to cause you to obsess about what you eat in any way, you will need to either change your approach or mind-set. Either way, remember this situation is primarily a battle of the mind you can win through Christ. (Phil 4:13)
If giving up food is a stumbling block to you, then consider fasting from television, reading (other than the Bible, of course), social media, or shopping. There are too many distractions and ways that we use to stay in control that we could eliminate from our daily routine. We do these things to distract ourselves from the real issues hurting us. If you can identify other things, maybe you can give those up instead of food.