Im fairly new to STO and learning new stuff every day. I decided to go for the nebular class because I love the ship and it's looks.

Im just a little confussed on how to arm it. I came from a cruiser and I prefer combat. This is how my equipment is atm

Fore weapons - Two Times. Dual Tetryon Beam Bank mk VI [Acc} {DMG and a Quantum Torpedo Launcher Mk VI {acc} x2

Deflector - Tachyon Deflector Array mk VI [Sen} [Stl} {ins}

Impulse - Hyper impulse engines mk VI {Aux} [Spd]

Sheilds - Covariant Shield Array mk VI {Cap] x2

Aft Weapons - 2x Tetryon beam array mk VI [Acc} x2

Engineering - Monotanium Alloy mk VI and Enginerring booster modulator mk vi

Science Consoles - Stealth module mk vi - Countermeasure system mk IV -

Tatical - Warhead Yield Chamber mk VI

I seam to be easily dameged and constantly using my science repair powers. The romulan ships seems to be doing alot off damege. Is there anyway I can improve my weapons or shields?

What Science skills do you use? I've just leveled an Engineer in a Nebula and found it was very effective against the Romulan NPCs. Like all NPCs they're very susceptible to power drains and will do nothing to clear debuffs so skills like subsystem targeting, Tyken's Rift and Gravity Well are very nice and make easy work of the NPCs.

For equipment, if you find you're taking a lot of damage the first thing I'd look at is a Resilient shield; it has less capacity than the Covariant you have but it takes only 5% bleed through damage (usually 10%) which can make a mess of the weaker Science ship hulls. If you only PvE then a Resilient shield with the [Dis] modifier will help by reducing Disruptor damage by 20%.
Weapons are personal preference but I prefer beam arrays and torpedoes, usually 2xBA and a Torpedo at each end. Again it's personal preference but it works for me so I run with it.
The Deflector looks as though it's not really going to be helping you at low levels. it has no [FlwC] modifier to help your inate subsystem targeting skills, the slight stealth sight increase isn't overly useful for PvE and the Romulan NPCs don't use any power drains for the Power Insulator buff to help against. Ideally you'd use a Deflector which increases the stats related to the skills you use but I don't have those details to recommend one.
The Engine looks like it'd be OK but in a Science ship you're probably running low engine power and at lower levels you won't have access to the Engine Performance skills so you'll not benefit from the engines speed at higher power levels. I always run a Combat Impulse Engine at that level and keep the power setting at 25. My ship may be slow but my skills benefit from the higher Aux level.

Consoles I tend to run those that increase the skills I use or buff important abilities. IIRC my Console layout at Commander was as follows;

Engineering

• Diburnium Armour
• RCS Accelerator

Science

• Shield Emitter console
• Shield Emitter console

Tactical

• Phaser Relay

At the lower levels the consoles are very weak so I just ran defensive consoles with the exception of the RCS which was only there to help with getting the nose on target (for the Tyken's). You didn't mention your class but this was for an Engineer (hence the Shield consoles which buffed my RSF) but it should help Science as well.
The Nebula was a good choice though, a really fun ship to use and surprisingly tough too. I have my Engineer rapidly approaching VA now in the T5 version and the practice at lower levels really helped, it's a very effective ship.