I wanted to know if you all think that it'd be best to find a way to work around using candles in rituals or if I should try and use candles anyways.
Well, that depends a lot on what you want your ritual practice and religious life to look at.
If you are working on your own, and if you are willing to be flexible about some elements of ritual practice, there are, as noted, LED candles and other ways to substitute for candles in ritual. (And I'm going to talk about a few options below.)
If, however, you think you might want to follow a specific tradition's set of practices, or you think you might want to attend public Wiccan-based rituals (or a number of other kinds, but I'm looking at your religion note in your profile), then not being comfortable around lit candles is going to limit your options some. Quite possibly a lot.
Fire is - like all four of the basic magical elements - a very powerful force. And a lot of people are really stupid about fire safety in ritual, so it's very appropriate to take necessary precautions.
But at the same time, fire in appropriate uses is - well, one of the fundamentals of civilisation. It's the light from the sun, it's the lightbulb in the dark, it's what lets us cook food, and do all sorts of other things.
So, one of the things you could think about over time is working on some of the general anxiety about it. (Are you seeing a therapist for anxiety in general?). Someone with training can help you work through specific fears until you can deal with candles in appropriate uses.
There's also plenty you can do that might be more achievable for you: it's totally appropriate to have a sacred fire extinguisher near the altar. It's fine to have, say, *one* candle, on a very stable table, in a glass container so that even if the candle tips, nothing bad will happen, rather than half a dozen. It's fine to be very careful about where the candle's placed (so nothing can fall into it/etc.)
Some fire departments offer fire safety workshops for the community on a regular basis. You might think about whether one of those (or a first aid/emergency response class) might help you deal with some of your anxiety. (For some people, first aid classes can make anxiety worse, but for some people, knowing that they've talked through what to do for different kinds of emergencies helps a lot.)
There are also some more ritual-type things that might help (though with someone with a known strong phobia, it's the kind of thing that I'd suggest doing only with a good relationship with a therapist in place, so that if something comes up that's too much to work through on your own, you already have help.) But one of the things people can do in ritual is work through *why* they're afraid of something.
There might be an old memory (or some people would consider a past life echo, or something like that) that has changed how you react to fire, and once you addressed that, your conscious mind might be able to deal better. (This is one of those things where if you only have a couple of strong anxiety triggers, it might be helpful to poke at them individually, but if you have a lot of anxiety that's triggered by a lot of different things, you probably want to address the anxiety in general first.)
Ritual bits. There's a lot of different reasons for using candles in ritual, and some of them are more easily substituted than others. (And which ones matter will depend a lot on your specific practices and/or tradition and/or path.)
(My ritual practices, based on my tradition's practices, involve fire as a representation of the element in circle, candles for use of the entities invited, and incense being lit from a candle, and for elemental work among others. The other effects of having candles are also nice, but they're not the reasons we use them.)
Fire as representation of the element in ritual: This is the one that it's hardest to find a clear substitute for, in many ways. However, some people find that an LED candle (electricity = fire in some ways) works for them. Some people find that say, glass works for them, or a piece of obsidian (both of which also have strong connections to earth, but are formed in fire.)
I'm also fond of a bunch of lengths of thin colored ribbon (the kind you get for $1-3 a roll at a craft store) in 4-5 appropriate colors (for fire, you might have yellow, orange, two shades of red) that you can hang or coil on an altar. It's got more vibrancy than many other objects. (I find 3-4 feet is a good length, and you want at least 15-20 strands.)
Fire as part of other ritual actions, like incense: Again, depends on ritual practice heavily - in my tradition, we use a lit incense stick for a specific ritual action, and there's just no way to duplicate it with, say, a simmering pot or perfumed oil or whatever. (It would be possible to rework the ritual bit, but it would take larger negotiation with other people, not just one person going "here's how we do it now.")
Candle as an anchor for deity or an elemental being: Some paths uses candles as a place for entities in circle to 'sit' - a place set aside just for them. The trick is that you wnat something that clearly indicates if there's something there or not (or welcome there) - and a candle obviously has a lit and unlit state. When we haven't been able to use candles, I've used small decorated boxes (the kind you can get for a couple of dollars at a craft store) that are opened when we would have lit a candle, and closed when we would have extinguished it.
Elemental focus: Some traditions have practices around attuning to a specific element for a period of time/season of the year/whatever. (Slightly different than representation in ritual.) Depending on your method, this can have different applications, and maybe a candle when it's the direct focus may feel different than as a part of a larger ritual process.
Candle for meditation: You can use an LED candle here easily, or a bowl of water, or whatever else you find an appropriate focus (some people like rocks, some people like a clear bit of glass, some people just close their eyes, etc.)
Light: Obviously, there are lots of alternatives. For dim ritual-friendly lighting, I am fond of either strings of white Christmas-type lights (they tend to go on sale right after Christmas) or paper-shaded lamps, but obviously, all sorts of options.
For pretty: Obviously, there are lots of other pretty things! Even shiny pretty things. Glass, often a good option here.