Can I replace a 15 ampere circuit breaker with a 20 ampere breaker?

No!

The only safe way to increase the circuit's capacity is by replacing the wire with one of adequate gauge. For 20 amps, 12 AWG copper is adequate for up to about 100 feet.

If you simply replace the breaker, the wire can overheat and ignite the building from inside the walls.

To resolve the dimming issue, check that the outlet is in good condition and that the wires are securely fastened and not showing any signs of overheating: blackening or loss of the copper shininess. Also, check the end of the wire inside the service panel, both neutral and "hot" (black) wire. If those are okay, set the appliances to a lower wattage setting or replace them with lower wattage models.

It's like this... Wireing is sort of like tubes you use to run water. Breakers are like an on off valve that also controls how much water(electricity) can to into the tube(wire). If you force too much water in a tube, it breaks and water gets everywhere. If you force to much electricity in a wire it breaks(melts) and gets fire everywhere. Fire is a lot more of a pain to clean.

perhaps you can but please let the competent person to do it.firstly the wire must be in good order and do not use too many apliances with higher wattage at the same time.The best is to buy you a new mcb with the same rating to replace the old one,generally this will solve most of similar iissue.

Absolutely NOT.

National Fire Protection Agency (NFPA) Standard Number 70, National Electric Code (NEC), adopted by most states (exceptions are Missouri, Mississippi and Arizona), requires the branch circuit Over Current Protection Device (OCPD --typically a circuit breaker (CB) nowadays, rather than a fuse from days of yore) to protect the cable/wiring buried in your walls from overheating by de-energizing (shut off/open circuit) all outlets (lighting & receptacles) for that circuit by tripping/blowing.

Lights dimming and CBs popping is a sure sign your house was not built to handle heating blankets and hair dryers in the bedroom. Swapping out a 20 amp breaker for the 15 amp breaker will violate NEC 210.19(A)(1) and provide cause for your insurance company not to reimburse your losses from fire & smoke damage and the water damage from the fire department flooding your house.

Wire is made smaller when manufactured by drawing/stretching it. The more times its stretched the smaller it gets. This is why American Wire Gauge (AWG) seems backwards, i.e. 14AWG has a smaller diameter than 10AWG because it was stretched more.

15 amp rated circuit breakers use 14 AWG current carrying conductors (black hot & white neutral) + a green ground wire which normally carries no current in industry standard outer white non-metallic sheathed cable called NM-B 90 degree Centigrade rated "Romex".

20 amp rated circuit breakers use the same configuration but 12 AWG, which is a larger diameter wire than 14 AWG, and therefor has less resistance for the same distance/footage from the load center/panelboard circuit breakers. 12 AWG NM-B sheathing is colored yellow.

10 AWG with orange sheathing would be even better electrically, but more expensive and not required by "code", the NEC.

Blame all this mumbo jumbo on Physics and a German named Georg Simon Ohm who created a Law that even Donald J. Trump can't repeal. Voltage loss (V) = current (i amps) times resistance (r ohms). And Power loss = current squared (i to the twoth power) times resistance (R).

When you draw too much current through a skinny wire, since its not a superconductor, you're converting electrical energy into heat energy from Ohm's resistive loss, resulting in less electrical energy (a voltage drop) reaching your load (appliance, light bulb, stereo, ...). The excess heat in the wire and inside your wall causes the insulation to fail over time, creating a potential short circuit accompanied by sparks that ignite flammables.

Have a licensed and insured electrician (Journeyman or Master) or electrical contractor add a new 20 amp circuit, or replace the existing 14 AWG cabling with 12 AWG cabling, or use your hair dryer in the bathroom which should already have a GFCI per NEC 210.8(A)1) and 20 amp receptacle per NEC 210.11(C)3) installed within three feet of the edge of a basin per NEC Article 200, Section III Required Outlets, 210.52 Dwelling Unit Receptacle Outlets, (D) Bathroom.

When it gets cold I put on an additional non-electric blanket, long thermal underwear, a hat and scarf, and let the dog sleep on the bed with me.

During the winter you might want to become a "snow bird" and fly south to Florida instead of having to deal with electricity, aka "Organized Lighting" according to George Carlin.